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This paper presents an evaluation of the wave function coefficients for conformally coupled scalars at both one and two-loop levels at leading order in the coupling constant, in momentum space. We take cues from time-dependent interactions in flat spacetime and under suitable approximations, these can also be used to study the wave function coefficients for general cosmologies. We make use of recursion relations developed in [20] to regularize certain bulk-point integrals and express the wave function coefficients in a form that simplifies the loop integrals. We utilize hard-cutoff regularization to regularize the loop integrals and further provide a discussion on their renormalization. Our results can also be analytically continued to obtain answers for transition amplitudes in AdS. [ABSTRACT FROM AUTHOR]

In this paper, we analyze the loop corrections to celestial OPE for gluons and gravitons. Even at the loop level, the soft gluons and gravitons have conformal dimensions ∆ = 1 − . The only novelty is the presence of higher poles. At one loop level, there are two types of conformal soft gluons with a single pole and a double pole in the ∆ plane. The celestial OPEs are obtained using the collinear splitting functions. In the case of gluons, the splitting functions receive loop corrections. After taking the holomorphic soft limit, we find the OPE of conformal soft gluons. We find a novel mixing of simple and double poles soft gluon operators in the OPE. In the case of gravitons, where splitting functions are known to be all loop exact, we still find a wedge algebra of w∞ which is in addition to the wedge algebra of w1+∞ already found by Strominger. [ABSTRACT FROM AUTHOR]

In this paper, we set up the numerical S-matrix bootstrap by using the crossing symmetric dispersion relation (CSDR) to write down Roy equations for the partial waves. As a motivation behind examining the local version of the CSDR, we derive a new crossing symmetric, 3-channels-plus-contact-terms representation of the Virasoro-Shapiro amplitude in string theory that converges everywhere except at the poles. We then focus on gapped theories and give novel analytic and semi-analytic derivations of several bounds on low-energy data. We examine the high-energy behaviour of the experimentally measurable rho-parameter, introduced by Khuri and Kinoshita and defined as the ratio of the real to the imaginary part of the amplitude in the forward limit. Contrary to expectations, we find numerical evidence that there could be multiple changes in the sign of this ratio before it asymptotes at high energies. We compare our approach with other existing numerical methods and find agreement, with improvement in convergence. [ABSTRACT FROM AUTHOR]

Celestial holography is a new way to understand flat-space amplitudes. Self-dual theories, due to their nice properties, are good subjects to study celestial holography. In this paper, we developed a new formula to calculate the celestial color-ordered self-dual Yang-Mills amplitudes based on celestial Berends-Giele currents, which makes the leading OPE limit manifest. In addition, we explore some higher-order terms of OPE in the celestial self-dual Yang-Mills theory. [ABSTRACT FROM AUTHOR]

The field-theoretic wavefunction has received renewed attention with the goal of better understanding observables at the boundary of de Sitter spacetime and studying the interior of Minkowski or general FLRW spacetime. Understanding the analytic structure of the wavefunction potentially allows us to establish bounds on physical observables. In this paper we develop an "amplitude representation" for the flat space wavefunction, which allow us to write the flat space wavefunction as an amplitude-like Feynman integral integrated over an energy-fixing kernel. With this representation it is possible to separate the wavefunction into an amplitude part and a subleading part which is less divergent as the total energy goes to zero. In turn the singularities of the wavefunction can be classified into two sets: amplitude-type singularities, which can be mapped to singularities found in amplitudes (including anomalous thresholds), and wavefunction-type singularities, which are unique to the wavefunction. As an example we study several tree level and one loop diagrams for scalars, and explore their singularities in detail. [ABSTRACT FROM AUTHOR]

This paper derives a next-to-leading power (NLP) soft theorem for multi-photon emission to all orders in the electromagnetic coupling constant, generalising the leading-power theorem of Yennie, Frautschi, and Suura. Working in the QED version of heavy-quark effective theory, multi-emission amplitudes are shown to reduce to single- and double-radiation contributions only. Single soft-photon emission, in turn, is described by the recent all-order extension of the Low-Burnett-Kroll theorem, where the tree-level formula is supplemented with a one-loop exact soft function. The same approach is used in this article to prove that the genuine double-emission contribution is tree-level exact. As a validation and a first non-trivial application of the multi-photon theorem, the real-real-virtual electron-line corrections to muon-electron scattering are calculated at NLP in the soft limit. [ABSTRACT FROM AUTHOR]

In this paper, we define the momentum amplituhedron in the four-dimensional split-signature space of dual momenta. It encodes scattering amplitudes at tree level and loop integrands for N = 4 super Yang-Mills in the planar sector. In this description, every point in the tree-level geometry is specified by a null polygon. Using the null structure of this kinematic space, we find a geometry whose canonical differential form produces loop-amplitude integrands. Remarkably, at one loop it is a curvy version of a simple polytope, whose vertices are specified by maximal cuts of the amplitude. This construction allows us to find novel formulae for the one-loop integrands for amplitudes with any multiplicity and helicity. The formulae obtained in this way agree with the ones derived via prescriptive unitarity. It makes prescriptive unitarity naturally emerge from this geometric description. [ABSTRACT FROM AUTHOR]

In this paper we focus on the orthogonal momentum amplituhedron O k, a recently introduced positive geometry that encodes the tree-level scattering amplitudes in ABJM theory. We generate the full boundary stratification of O k for various k and conjecture that its boundaries can be labelled by so-called orthogonal Grassmannian forests (OG forests). We determine the generating function for enumerating these forests according to their dimension and show that the Euler characteristic of the poset of these forests equals one. This provides a strong indication that the orthogonal momentum amplituhedron is homeomorphic to a ball. This paper is supplemented with the Mathematica package orthitroids which contains useful functions for exploring the structure of the positive orthogonal Grassmannian and the orthogonal momentum amplituhedron. [ABSTRACT FROM AUTHOR]

The Coon amplitude is a q-deformed generalization of the Veneziano amplitude exhibiting a semi-infinite sequence of poles that converge on an accumulation point, from which a branch cut emerges. A number of recent papers have provided compelling evidence that the residues of this amplitude satisfy the positivity requirements imposed by unitarity. This paper investigates whether positivity is also satisfied along the branch cut. It is demonstrated for a wide range of q-values that positivity violations occur in a region of the branch cut exponentially close to the accumulation point according to a scale set by q. The closing section of the paper discusses possible interpretations of this fact and strategies for excising negativity from the partial wave coefficients. An appendix presents derivations of instrumental identities relating the q-gamma and q-polygamma functions to the Weierstrass elliptic and quasiperiodic functions. [ABSTRACT FROM AUTHOR]

Ambitwistor-strings are chiral strings whose targets are spaces of complex massless particles, and whose correlation functions directly lead to simple, compact formulae for scattering amplitudes and loop integrands for massless gauge and gravity theories. This article extends the framework to massive particles in 4d, obtained via a symmetry reduction of higher dimensional massless models based on twistors. The target space of the resulting models turns out to be the phase space of 4d massive particles in a twistorial representation, and the worldsheet theory agrees with the two-twistor string previously introduced by the authors. The paper has been written so as to be largely self-contained. We discuss two interesting classes of massive theories in detail. For gauge theories, the reduction procedure is explicitly adapted to supersymmetric gauge theories on the Coulomb branch. For supergravity theories, the reduction is adapted to give theories obtained via Cremmer, Scherk & Schwartz (CSS) reduction, with broken supersymmetry and massive multiplets. The reduction procedure gives explicit and systematic rules to obtain amplitudes for all these theories and their amplitudes from two compact master formulae that have their origins in 6d based on the polarized scattering equations; in the CSS case the formulae are new, and in both cases their derivation is systematic. The freedom to include mass allows the definition of a loop insertion operator, thereby extending the formulae to 1-loop. Unlike the massless 4d twistorial models, these all display a perfect double copy structure, here incorporating massive particles in the relationship between gauge theory and CSS supergravity amplitudes. [ABSTRACT FROM AUTHOR]

Celestial amplitudes obtained from Mellin transforming 4d momentum space scattering amplitudes contain distributional delta functions, hindering the application of conventional CFT techniques. In this paper, we propose to bypass this problem by recognizing Mellin transforms as integral transforms projectivizing certain components of the angular momentum. It turns out that the Mellin transformed wavefunctions in the conformal primary basis can be regarded as representatives of certain cohomology classes on the minitwistor space of the hyperbolic slices of 4d Minkowski space. Geometrically, this amounts to treating 4d Minkowski space as the embedding space of AdS3. By considering scattering of such on-shell wavefunctions on the projective spinor bundle ℙ핊 of Euclidean AdS3, we bypass the difficulty of the distributional properties of celestial correlators using the traditional AdS3/CFT2 dictionary and find conventional 2d CFT correlators for the scaling reduced Yang-Mills theory living on the hyperbolic slices. In the meantime, however, one is required to consider action functionals on the auxiliary space ℙ핊, which introduces additional difficulties. Here we provide a framework to work on the projective spinor bundle of hyperbolic slices, obtained from a careful scaling reduction of the twistor space of 4d Minkowski spacetime. [ABSTRACT FROM AUTHOR]

In this paper, we study celestial amplitudes of Goldstone bosons and conformal soft theorems. Motivated by the success of soft bootstrap in momentum space and the important role of the soft limit behavior of tree-level amplitudes, our goal is to extend some of the methods to the celestial sphere. The crucial ingredient of the calculation is the Mellin transformation, which transforms four-dimensional scattering amplitudes to correlation functions of primary operators in the celestial CFT. The soft behavior of the amplitude is then translated to the singularities of the correlator. Only for amplitudes in "UV completed theories" (with sufficiently good high energy behavior) the Mellin integration can be properly performed. In all other cases, the celestial amplitude is only defined in a distributional sense with delta functions. We provide many examples of celestial amplitudes in UV-completed models, including linear sigma models and Z-theory, which is a certain completion of the SU(N) non-linear sigma model. We also comment on the BCFW-like and soft recursion relations for celestial amplitudes and the extension of soft bootstrap ideas. [ABSTRACT FROM AUTHOR]

This paper presents a systematic cataloging of the generators of celestial symmetries on phase space. Starting from the celestial OPEs, we first show how to extract a representation of the general-spin analog of the wedge subalgebra of w1+∞ on the phase space of massless matter fields of arbitrary helicity. These generators can be expressed as light-sheet operators that are quadratic in the matter fields at future or past null infinity. We next show how to extend these symmetries beyond the wedge. Doing so requires us to augment the quadratic operators with: 1) linear terms corresponding to primary descendants of the negative helicity gauge fields the matter modes couple to, and 2) a tower of higher-particle composite operator contributions. These modes can be realized as light-ray operators supported on generators of null infinity, but local on the celestial sphere. Finally, we construct a representation of the celestial symmetries that captures how the positive helicity gauge fields transform. We close by discussing how these celestial symmetries inform our choice of detector operators. [ABSTRACT FROM AUTHOR]

In this paper we focus on scattering amplitudes in maximally supersymmetric Yang-Mills theory and define a long sought-after geometry, the loop momentum amplituhedron, which we conjecture to encode tree and (the integrands of) loop amplitudes in spinor helicity variables. Motivated by the structure of amplitude singularities, we define an extended positive space, which enhances the Grassmannian space featuring at tree level, and a map which associates to each of its points tree-level kinematic variables and loop momenta. The image of this map is the loop momentum amplituhedron. Importantly, our formulation provides a global definition of the loop momenta. We conjecture that for all multiplicities and helicity sectors, there exists a canonical logarithmic differential form defined on this space, and provide its explicit form in a few examples. [ABSTRACT FROM AUTHOR]

This paper presents a calculation of the four gravitons amplitude in (Anti)-de Sitter space, focusing specifically on external gravitons with positive helicity. To achieve this, we employ a generalized recursion method that involves complexifying all external momentum of the graviton function, which results in the factorization of AdS graviton amplitudes and eliminates the need for Feynman-Witten diagrams. Our calculations were conducted in three boundary dimensions, with a particular emphasis on exploring cosmology and aiding the cosmological bootstrap program. To compute the expression, we utilized the three-dimensional spinor helicity formalism. The final expression was obtained by summing over residues of physical poles, and we present both symbolic and numerical results. Additionally, we discuss the advantages and limitations of this approach, and highlight potential opportunities for future research. [ABSTRACT FROM AUTHOR]

As a key method to deal with loop integrals, Integration-By-Parts (IBP) method can be used to do reduction as well as establish the differential equations for master integrals. However, when talking about tensor reduction, the Passarino-Veltman (PV) reduction method is also widely used for one-loop integrals. Recently, we have proposed an improved PV reduction method, i.e., the PV reduction method with auxiliary vector R, which can easily give analytical reduction results for any tensor rank. However, our results are only for integrals with propagators with power one. In this paper, we generalize our method to one-loop integrals with general tensor structures and propagators with general powers. Our ideas are simple. We solve the generalised reduction problem by combining differentiation over masses and proper limit of reduction with power-one propagators. Finally, we demonstrate our method with several examples. With the result in this paper, we have shown that our improved PV-reduction method with auxiliary vector is a self-completed reduction method for one-loop integrals. [ABSTRACT FROM AUTHOR]

Two-loop corrections to scattering amplitudes are crucial theoretical input for collider physics. Recent years have seen tremendous advances in computing Feynman integrals, scattering amplitudes, and cross sections for five-particle processes. In this paper, we initiate the study of the function space for planar two-loop six-particle processes. We study all genuine six-particle Feynman integrals, and derive the differential equations they satisfy on maximal cuts. Performing a leading singularity analysis in momentum space, and in Baikov representation, we find an integral basis that puts the differential equations into canonical form. The corresponding differential equation in the eight independent kinematic variables is derived with the finite-field reconstruction method and the symbol letters are identified. We identify the dual conformally invariant hexagon alphabet known from maximally supersymmetric Yang-Mills theory as a subset of our alphabet. This paper constitutes an important step in the analytic calculation of planar two-loop six-particle Feynman integrals. [ABSTRACT FROM AUTHOR]

In this paper, we develop an iterative sector-level reduction strategy for Feynman integrals, which bases on module intersection in the Baikov representation and auxiliary vector for tensor structure. Using this strategy we have studied the reduction of general one-loop integrals, i.e., integrals having arbitrary tensor structures and arbitrary power for propagators. Inspired by these studies, a uniform and compact formula that iteratively reduces all one-loop integrals has been written down, where messy polynomials in integration-by-parts (IBP) relations have organized themselves to Gram determinants. [ABSTRACT FROM AUTHOR]

In [1], logarithmic correction to subleading soft photon and soft graviton theorems have been derived in four spacetime dimensions from the ratio of IR-finite S-matrices. This has been achieved after factoring out IR-divergent components from the traditional electromagnetic and gravitational S-matrices using Grammer-Yennie prescription. Although the loop corrected subleading soft theorems are derived from one-loop scattering amplitudes involving scalar particles in a minimally coupled theory with scalar contact interaction, it has been conjectured that the soft factors are universal (theory independent) and one-loop exact (don't receive corrections from higher loops). This paper extends the analysis conducted in [1] to encompass general spinning particle scattering with non-minimal couplings permitted by gauge invariance and general coordinate invariance. By re-deriving the ln ω soft factors in this generic setup, we establish their universal nature. Furthermore, we summarize the results of loop corrected soft photon and graviton theorems up to sub-subleading order, which follows from the analysis of one and two loop QED and quantum gravity S-matrices. While the classical versions of these soft factors have already been derived in the literature, we put forth conjectures regarding the quantum soft factors and outline potential strategies for their derivation. [ABSTRACT FROM AUTHOR]

In this paper we provide a detailed account of our calculation, briefly reported in arXiv:2209.09263, of a two-particle form factor of the lowest components of the stress-tensor multiplet in N = 4 sYM theory on its Coulomb branch, which is interpreted as an off-shell kinematical regime. We demonstrate that up to three-loop order, both its infrared-divergent as well as finite parts do exponentiate in the Sudakov regime, with the coefficient accompanying the double logarithm being determined by the octagon anomalous dimension Γoct. We also observe that up to this order in 't Hooft coupling the logarithm of the Sudakov form factor is identical to twice the logarithm of the null octagon, which was introduced within the context of integrability-based computation of four point correlators with infinitely large R-charges. The null octagon is known in a closed form for all values of the 't Hooft coupling constant and kinematical parameters. We conjecture that the relation between the former and the off-shell Sudakov form factor holds to all loop orders. [ABSTRACT FROM AUTHOR]

We introduce a novel point-particle effective description of ANO vortex solitons in the critical Abelian Higgs Model (AHM) in d = 2 + 1 based on the small winding expansion. Identifying the effective vortices with the elementary quanta of a complex scalar field, relativistic vortex-vortex scattering amplitudes are calculated as a diagrammatic, perturbative expansion in the winding number N. Making use of powerful techniques recently developed for analyzing the post-Minkowskian two-body problem in general relativity, we efficiently extract the contribution to the loop integrals from the classical potential region, with the resulting velocity expansion subsequently resummed to all orders. The main result of this paper is an analytic expression for the classical, vortex-vortex potential at O (N2), or one-loop, with exact velocity dependence. By truncating the resulting effective Hamiltonian at O (p2) we derive an analytic, perturbative expression for the metric on the 2-vortex moduli space. Finally, the emergence of the critical AHM from the classical limit of the N = 2 supersymmetric AHM, and the resulting constraints on the point-particle EFT is described in detail using an on-shell superspace construction for BPS states in d = 2 + 1. [ABSTRACT FROM AUTHOR]

We perform a complete and systematic analysis of the solution space of six-dimensional Einstein gravity. We show that a particular subclass of solutions — those that are analytic near I + — admit a non-trivial action of the generalised Bondi-Metzner-van der Burg-Sachs (GBMS) group which contains infinite-dimensional supertranslations and superrotations. The latter consists of all smooth volume-preserving Diff×Weyl transformations of the celestial S4. Using the covariant phase space formalism and a new technique which we develop in this paper (phase space renormalization), we are able to renormalize the symplectic potential using counterterms which are local and covariant. The Hamiltonian charges corresponding to GBMS diffeomorphisms are non-integrable. We show that the integrable part of these charges faithfully represent the GBMS algebra and in doing so, settle a long-standing open question regarding the existence of infinite-dimensional asymptotic symmetries in higher even dimensional non-linear gravity. Finally, we show that the semi-classical Ward identities for supertranslations and superrotations are precisely the leading and subleading soft-graviton theorems respectively. [ABSTRACT FROM AUTHOR]

We present compact analytic results for tree-level amplitudes containing a t t ¯ pair accompanied by up to four massless partons, t t ¯ gg , t t ¯ ggg , t t ¯ gggg , t t ¯ q q ¯ , t t ¯ q q ¯ g , t t ¯ q q ¯ gg and t t ¯ q q ¯ q ′ q ¯ ′ . The results, obtained using BCFW on-shell recursion, are based both on previous published results and on the new calculations performed in this paper. These amplitudes are sufficient to calculate the production of a t t ¯ pair and zero, one, or two light parton jets, with the option to include the tree-level decays t → bνe+ and t ¯ → b ¯ e − ν ¯ efficiently. Our results are part of the NNLO corrections to t t ¯ production including the decay correlations for on-shell top quarks. [ABSTRACT FROM AUTHOR]

In the Grassmannian formulation of the S-matrix for planar N = 4 Super Yang-Mills, Nk−2MHV scattering amplitudes for k negative and n − k positive helicity gluons can be expressed, by an application of the global residue theorem, as a signed sum over a collection of (k − 2)(n − k − 2)-dimensional residues. These residues are supported on certain positroid subvarieties of the Grassmannian G(k, n). In this paper, we replace the Grassmannian G(3, n) with its torus quotient, the moduli space of n points in the projective plane in general position, and planar N = 4 SYM with generalized biadjoint scalar amplitudes m n 3 as introduced by Cachazo-Early-Guevara-Mizera (CEGM) [1]. Whereas in the Grassmannian formulation residues of the Parke-Taylor form correspond to individual BCFW, or on-shell diagrams, we show that each such (n − 5)-dimensional residue of m n 3 an entire biadjoint scalar partial amplitude m n 2 , that is a sum over all tree-level Feynman diagrams for a fixed planar order. We make a proposal which would do the same for k ≥ 4. [ABSTRACT FROM AUTHOR]

In this paper we study the tree-level OPE between two positive helicity outgoing gluons in the celestial CFT for the Yang-Mills theory chirally coupled to a massive scalar background. This theory breaks the translation as well as scale invariance. We compute the subleading terms in the OPE expansion and show that they are same as the subleading terms of the OPE expansions in the MHV sector. As a result the amplitudes of this theory also satisfy the set of differential equations obtained previously for MHV amplitudes in pure YM theory. This is not surprising because the symmetries coming from the leading and subleading soft gluon theorems do not change in the presence of a massive scalar background. [ABSTRACT FROM AUTHOR]

Celestial amplitude plays an important role in the understanding of holography. Computing celestial amplitudes by recursion can deepen our understanding of the structure of celestial amplitudes. As an important recursion method, the Berends-Giele (BG) currents on the celestial sphere are worth studying. In this paper, we study the celestial BG recursion and utilize this to calculate some typical examples. We also explore the OPE behavior of celestial BG currents. Moreover, we generalize the “sewing procedure” for BG currents to the celestial case. [ABSTRACT FROM AUTHOR]

In this paper, we investigate two-loop non-planar triangle Feynman integrals involving elliptic curves. In contrast to the Sunrise and Banana integral families, the triangle families involve non-trivial sub-sectors. We show that the methodology developed in the context of Banana integrals can also be extended to these cases and obtain ε-factorized differential equations for all sectors. The letters are combinations of modular forms on the corresponding elliptic curves and algebraic functions arising from the sub-sectors. With uniform transcendental boundary conditions, we express our results in terms of iterated integrals order-by-order in the dimensional regulator, which can be evaluated efficiently. Our method can be straightforwardly generalized to other elliptic integral families and have important applications to precision physics at current and future high-energy colliders. [ABSTRACT FROM AUTHOR]

In this paper, we take a major step towards the construction and applications of an all-loop, all-multiplicity amplituhedron for three-dimensional planar N = 6 Chern-Simons matter theory, or the ABJM amplituhedron. We show that by simply changing the overall sign of the positive region of the original amplituhedron for four-dimensional planar N = 4 super-Yang-Mills (sYM) and performing a symplectic reduction, only three-dimensional kinematics in the middle sector of even-multiplicity survive. The resulting form of the geometry, combined with its parity images, gives the full loop integrand. This simple modification geometrically enforces the vanishing of odd-multiplicity cuts, and manifests the correct soft cuts as well as two-particle unitarity cuts. Furthermore, the so-called “bipartite structures” of four-point all-loop negative geometries also directly generalize to all multiplicities. We introduce a novel approach for triangulating loop amplituhedra based on the kinematics of the tree region, resulting in local integrands tailored to “prescriptive unitarity”. This construction sheds fascinating new light on the interplay between loop and tree amplituhedra for both ABJM and N = 4 sYM: the loop geometry demands that the tree region must be dissected into chambers, defined by the simultaneous positivity of maximal cuts. The loop geometry is then the “fibration” of the tree region. Using the new construction, we give explicit results of one-loop integrands up to ten points and two-loop integrands up to eight points by computing the canonical form of ABJM loop amplituhedron. [ABSTRACT FROM AUTHOR]

We recently introduced in [9] a boundary-to-bound dictionary between gravitational scattering data and observables for bound states of non-spinning bodies. In this paper, we elaborate further on this holographic map. We start by deriving the following — remarkably simple — formula relating the periastron advance to the scattering angle: ΔΦ J E = χ J E + χ − J E , via analytic continuation in angular momentum and binding energy. Using explicit expressions from [9], we confirm its validity to all orders in the Post-Minkowskian (PM) expansion. Furthermore, we reconstruct the radial action for the bound state directly from the knowledge of the scattering angle. The radial action enables us to write compact expressions for dynamical invariants in terms of the deflection angle to all PM orders, which can also be written as a function of the PM-expanded amplitude. As an example, we reproduce our result in [9] for the periastron advance, and compute the radial and azimuthal frequencies and redshift variable to two-loops. Agreement is found in the overlap between PM and Post-Newtonian (PN) schemes. Last but not least, we initiate the study of our dictionary including spin. We demonstrate that the same relation between deflection angle and periastron advance applies for aligned-spin contributions, with J the (canonical) total angular momentum. Explicit checks are performed to display perfect agreement using state-of-the-art PN results in the literature. Using the map between test- and two-body dynamics, we also compute the periastron advance up to quadratic order in spin, to one-loop and to all orders in velocity. We conclude with a discussion on the generalized ‘impetus formula’ for spinning bodies and black holes as ‘elementary particles’. Our findings here and in [9] imply that the deflection angle already encodes vast amount of physical information for bound orbits, encouraging independent derivations using numerical and/or self-force methodologies. [ABSTRACT FROM AUTHOR]

Both celestial and momentum space amplitudes in four dimensions are beset by divergences resulting from spacetime translation and sometimes scale invariance. In this paper we consider a (linearized) marginal deformation of the celestial CFT for Yang-Mills theory which preserves 2D conformal invariance but breaks both spacetime translation and scale invariance and involves a chirally coupled massive scalar. The resulting MHV celestial amplitudes are completely finite (apart from the usual soft and collinear divergences and isolated poles in the sum of the weights) and take the canonical CFT form. Moreover, we show they can be simply rewritten in terms of AdS3-Witten contact diagrams which evaluate to the well-known D-functions, thereby forging a direct connection between flat and AdS holography. [ABSTRACT FROM AUTHOR]

In this paper we explore and expand the connection between two modern descriptions of scattering amplitudes, the CHY formalism and the framework of positive geometries, facilitated by the scattering equations. For theories in the CHY family whose S-matrix is captured by some positive geometry in the kinematic space, the corresponding canonical form can be obtained as the pushforward via the scattering equations of the canonical form of a positive geometry defined in the CHY moduli space. In order to compute these canonical forms in kinematic spaces, we study the general problem of pushing forward arbitrary rational differential forms via the scattering equations. We develop three methods which achieve this without ever needing to explicitly solve any scattering equations. Our results use techniques from computational algebraic geometry, including companion matrices and the global duality of residues, and they extend the application of similar results for rational functions to rational differential forms. [ABSTRACT FROM AUTHOR]

Multi-loop Feynman integrals are key objects for the high-order correction computations in high energy phenomenology. These integrals with multiple scales may have complicated symbol structures, and we show that twistor geometries of closely related dual conformal integrals shed light on their alphabet and symbol structures. In this paper, first, as a cutting-edge example, we derive the two-loop four-external-mass Feynman integrals with uniform transcendental (UT) weights, based on the latest developments on UT integrals. Then we find that all the symbol letters of these integrals can be explained non-trivially by studying the so-called Schubert problem of certain dual conformal integrals with a point at infinity. Certain properties of the symbol such as first two entries and extended Steinmann relations are also studied from analogous properties of dual conformal integrals. [ABSTRACT FROM AUTHOR]

Symbol alphabets of n-particle amplitudes in N = 4 super-Yang-Mills theory are known to contain certain cluster variables of G(4, n) as well as certain algebraic functions of cluster variables. The first paper arXiv:2007.00646 in this series focused on n = 8 algebraic letters. In this paper we show that it is possible to obtain all rational symbol letters (in fact all cluster variables) by solving matrix equations of the form C Z = 0 if one allows C to be an arbitrary cluster parameterization of the top cell of G+(n−4, n). [ABSTRACT FROM AUTHOR]

Recently a function was constructed that satisfies all known properties of a tree-level scattering of four massless scalars via the exchange of an infinite tower of particles with masses given by the non-trivial zeroes of the Riemann zeta function. A key ingredient in the construction is an even entire function whose only zeroes coincide with the non-trivial zeroes of the Riemann zeta function. In this paper we show that exactly the same conclusions can be drawn for an infinite class of even entire functions with only zeroes on the real line. This shows that the previous result does not seem to be connected to specific properties of the Riemann zeta function, but it applies more generally. As an application, we show that exactly the same conclusions can be drawn for L-functions other than the Riemann zeta function. [ABSTRACT FROM AUTHOR]

In this paper, we explore Bell inequality violation for 2 → 2 scattering in Effective Field Theories (EFTs) of photons, gluons, and gravitons. Using the CGLMP Bell parameter (I2), we show that, starting from an appropriate initial non-product state, the Bell inequality can always be violated in the final state (i.e.,I2> 2) at least for some scattering angle. For an initial product state, we demonstrate that abelian gauge theories behave qualitatively differently than non-abelian gauge theories (or Gravity) from the point of view of Bell violation in the final state: in the non-abelian case, Bell violation (I2> 2) is never possible within the validity of EFTs for weakly coupled UV completions. Interestingly, we also find that, for a maximally entangled initial state, scattering can reduce the degree of entanglement only for CP-violating theories. Thus Bell violation in 2 → 2 scattering can, in principle, be used to classify CP conserving vs violating theories. [ABSTRACT FROM AUTHOR]

A variety of condensed matter systems describe gapless modes that can be interpreted as Nambu-Goldstone bosons of spontaneously broken Poincaré symmetry. In this paper we derive new soft theorems constraining the tree-level scattering of these degrees of freedom, as exhibited in solids, fluids, superfluids, and framids. These soft theorems are in one-to-one correspondence with various broken symmetries, including spacetime translations, Lorentz boosts, and, for the case of fluids, volume-preserving diffeomorphisms. We also implement a bootstrap in which the enhanced vanishing of amplitudes in the soft limit is taken as an input, thus sculpting out a subclass of exceptional solid, fluid, and framid theories. [ABSTRACT FROM AUTHOR]

We present several classes of constraints on the discontinuities of Feynman integrals that go beyond the Steinmann relations. These constraints follow from a geometric formulation of the Landau equations that was advocated by Pham, in which the singularities of Feynman integrals correspond to critical points of maps between on-shell spaces. To establish our results, we review elements of Picard-Lefschetz theory, which connect the homotopy properties of the space of complexified external momenta to the homology of the combined space of on-shell internal and external momenta. An important concept that emerges from this analysis is the question of whether or not a pair of Landau singularities is compatible — namely, whether or not the Landau equations for the two singularities can be satisfied simultaneously. Under conditions we describe, sequential discontinuities with respect to non-compatible Landau singularities must vanish. Although we only rigorously prove results for Feynman integrals with generic masses in this paper, we expect the geometric and algebraic insights that we gain will also assist in the analysis of more general Feynman integrals. [ABSTRACT FROM AUTHOR]

In [1], we proposed a universal method to reduce one-loop integrals with both tensor structure and higher-power propagators. But the method is quite redundant as it does not utilize the results of lower rank cases when addressing certain tensor integrals. Recently, we found a remarkable recursion relation [2-3], where a tensor integral is reduced to lower-rank integrals and lower terms corresponding to integrals with one or more propagators being canceled. However, the expression of the lower terms is unknown. In this paper, we derive this non-trivial recursion relation for non-degenerate and degenerate cases and provides an explicit expression for the lower terms, thus simplifying and speeding up the reduction process. [ABSTRACT FROM AUTHOR]

Color-factor symmetry is a property of tree-level gauge-theory amplitudes containing at least one gluon. BCJ relations among color-ordered amplitudes follow directly from this symmetry. Color-factor symmetry is also a feature of biadjoint scalar theory amplitudes as well as of their equations of motion. In this paper, we present a new proof of color-factor symmetry using a recursive method derived from the perturbiner expansion of the classical equations of motion. [ABSTRACT FROM AUTHOR]

In hadron spectrum physics, the partial wave analysis is a primary method used to extract properties of hadronic resonances. The covariant orbital-spin coupling scheme holds unique advantages over other partial wave methods due to its Lorentz covariant form and determined orbital-spin quantum numbers. This paper presents a general form of the covariant orbital-spin coupling scheme based on the irreducible tensor of the homogeneous proper Lorentz group and its little groups. A systematic procedure for constructing partial wave amplitude in a Lorentz covariant way is provided, which can be applied to both massive and massless particles. Specific examples are also included. [ABSTRACT FROM AUTHOR]

In this paper we initiate the study of form factors for the massless scattering of integrable AdS2 superstrings, where the difference-form of the S-matrix can be exploited to implement the relativistic form factor bootstrap. The non-standard nature of the S-matrix implies that traditional methods do not apply. We use the fact that the massless AdS2S-matrix is a limit of a better-behaved S-matrix found by Fendley. We show that the previously conjectured massless AdS2 dressing factor coincides with the limit of the De Martino-Moriconi improved dressing factor for the Fendley S-matrix. We then solve the form factor constraints in the two-particle case. Along the way we find a method to construct integral representations of relativistic dressing factors satisfying specific assumptions, and use it to obtain analytic proofs of crossing and unitarity relations. [ABSTRACT FROM AUTHOR]

In this paper we develop and demonstrate a method to obtain epsilon factorized differential equations for elliptic Feynman integrals. This method works by choosing an integral basis with the property that the period matrix obtained by integrating the basis over a complete set of integration cycles is diagonal. The method is a generalization of a similar method known to work for polylogarithmic Feynman integrals. We demonstrate the method explicitly for a number of Feynman integral families with an elliptic highest sector. [ABSTRACT FROM AUTHOR]

Feynman integrals in quantum field theory evaluate to special functions and numbers that are usefully described by the notion of transcendental weight. In this paper, we propose a way of projecting a given dimensionally-regularised Feynman integral, for example contributing to a scattering amplitudes, onto its maximal weight part. The method uses insights into the singularity structure of space-time loop integrands, and is complementary to usual generalised unitarity approaches. We describe the method and give a proof-of-principle application to the two-loop scattering amplitudes gg → H in the heavy top-quark mass limit, which involves both planar and non-planar Feynman integrals. We also comment on further possible applications and discuss subtleties related to evanescent integrand terms. [ABSTRACT FROM AUTHOR]

It is well known that gravity amplitudes in four dimensions can be reconstructed by the inverse soft limit (ISL) method. According to ISL, a tree level n-graviton maximally-helicity-violating (MHV) amplitude is expressed in terms of deformed (n − 1)-graviton amplitudes accompanied by soft graviton factors. On another hand, single- and double-trace tree-level Einstein-Yang-Mills (EYM) MHV amplitudes have been proven to satisfy spanning forest formulas, where each edge in a forest has the same form with a term in soft graviton factor. It is not transparent that the formulas satisfied by EYM amplitudes can be constructed with ISL. In this paper, we construct the single- and double-trace MHV amplitudes in EYM, by the ISL and show that the known formulas can be precisely reproduced. Interesting identities which are based on Schouten identity and characterized by graphs are also introduced. [ABSTRACT FROM AUTHOR]

Carrollian Conformal Field Theories (CFTs) have been proposed as co-dimension one holographic duals to asymptotically flat spacetimes as opposed to Celestial CFTs which are co-dimension two. In this paper, drawing inspiration from Celestial holography, we show by a suitable generalisation of the flat space limit of AdS that keeps track of the previously disregarded null direction, one can reproduce Carrollian CFT correlation functions from AdS Witten diagrams. In particular, considering Witten diagrams in AdS4, we reproduce two and three-point correlation functions for three dimensional Carrollian CFTs in the so-called delta-function branch. Along the way, we construct non-trivial Carrollian three-point functions in the delta-branch by considering a collinear limit. We also obtain a generalised anti-podal matching condition that now depends on the retarded time direction. [ABSTRACT FROM AUTHOR]

Four point tree-level local S-matrices form a module over ring of polynomials of Mandelstam invariants s, t and u. The module of local analytic S-matrices can be encoded in terms of a partition function which is enumerated using plethystic techniques. In this paper, we enumerate the plethystic contribution to local four point photon, graviton and gluon multi-particle partition functions that encode parity violating 2 → 2 scattering. We generalise the counting problem solved in [1-2] to project out parity violating sectors, a subtle task in even dimensions [3]. We explicitly enumerate the parity odd contributions to the multi-letter partition function for gauge fields, gravitons and gluons and evaluate the resulting parity violating partition functions in D = 4, 6. We also perform a large D analysis to show that parity violating local interactions do not contribute to four particle scattering in higher dimensions (D ≥ 8). Our computations and observations for photons, gravitons and gluons agree with the transformation properties of these S-matrices previously conjectured in [1-2] [ABSTRACT FROM AUTHOR]

Classical soft theorems applied to probe scattering processes on AdS4 spacetimes predict the existence of perturbative 1/L2 corrections to the soft photon and soft graviton factors of asymptotically flat spacetimes. In this paper, we establish that the 1/L2 corrected soft photon theorem can be derived from a large N CFT3 Ward identity. We derive a perturbed soft photon mode operator on a flat spacetime patch in global AdS4 in terms of an integrated expression of the boundary CFT current. Using the same in the CFT3 Ward identity, we recover the 1/L2 corrected soft photon factor derived from classical soft theorems. [ABSTRACT FROM AUTHOR]

We investigate the perturbative integrability of different quantum field theories in 1+1 dimensions at one loop. Starting from massive bosonic Lagrangians with polynomial-like potentials and absence of inelastic processes at the tree level, we derive a formula reproducing one-loop inelastic amplitudes for arbitrary numbers of external legs. We show that any one-loop inelastic amplitude is equal to its tree-level version, in which the masses of particles and propagators are corrected by one-loop bubble diagrams. These amplitudes are nonzero in general and counterterms need to be added to the Lagrangian to restore the integrability at one loop. For the class of simply-laced affine Toda theories, we show that the necessary counterterms are obtained by scaling the potential with an overall multiplicative factor, proving in this way the one-loop integrability of these models. Even though we focus on bosonic theories with polynomial-like interactions, we expect that the on-shell techniques used in this paper to compute amplitudes can be applied to several other models. [ABSTRACT FROM AUTHOR]

On-shell kinematics for gluon scattering can be parametrized with points on the celestial sphere; in the limit where these points collide, it is known that tree-level gluon scattering amplitudes exhibit an operator product expansion (OPE)-like structure. While it is possible to obtain singular contributions to this celestial OPE, getting regular contributions from both holomorphic and anti-holomorphic sectors is more difficult. In this paper, we use twistor string theory to describe the maximal helicity violating (MHV) sector of tree-level, four-dimensional gluon scattering as an effective 2d conformal field theory on the celestial sphere. By organizing the OPE between vertex operators in this theory in terms of soft gluon descendants, we obtain all-order expressions for the celestial OPE which include all regular contributions in the collinear expansion. This gives new, all-order formulae for the collinear splitting function (in momentum space) and celestial OPE coefficients (in the conformal primary basis) of tree-level MHV gluon scattering. We obtain these results for both positive and negative helicity gluons, and for any incoming/outgoing kinematic configuration within the MHV sector. [ABSTRACT FROM AUTHOR]

A powerful aspect of effective field theories is connecting scales through renormalisation group (RG) flow. The anomalous dimension matrix of the Standard Model Effective Field Theory (SMEFT) encodes clues to where to find relics of heavy new physics in data, but its unwieldy 2499 × 2499 size (at operator dimension 6) makes it difficult to draw general conclusions. In this paper, we study the flavour structure of the SMEFT one loop anomalous dimension matrix of dimension 6 current-current operators, a 1460 × 1460 submatrix. We take an on-shell approach, laying bare simple patterns by factorising the entries of the matrix into their gauge, kinematic and flavour parts. We explore the properties of different diagram topologies, and make explicit the connection between the IR-finiteness of certain diagrams and their gauge and flavour structure. Through a completely general flavour decomposition of the Wilson coefficient matrices, we uncover new flavour selection rules, from which small subsystems emerge which mix almost exclusively amongst themselves. We show that, for example, if we neglect all Yukawa couplings except for that of the top quark, the selection rules produce block diagonalisation within the current-current operators in which the largest block is a 61 × 61 matrix. We provide all the ingredients of the calculations in comprehensive appendices, including SM and SMEFT helicity amplitudes, and explicit results for phase space integrals and gauge contractions. This deconstruction of the matrix, and its resulting block-diagonalisation, provides a first step to understanding the IR-relevant directions in the SMEFT parameter space, hence closing in on natural places for heavy new physics to make itself known. [ABSTRACT FROM AUTHOR]