Search

We study off-shell n-particle form factors of half-BPS operators built from n complex scalar fields at the two-loop order in the planar maximally supersymmetric Yang-Mills theory (sYM). These are known as minimal form factors. We construct their representation as a sum of independent scalar Feynman integrals relying on two complementary techniques. First, by going to the Coulomb branch of the theory by employing the spontaneous symmetry breaking which induces masses, but only for external particles while retaining masslessness for virtual states propagating in quantum loops. For a low number of external legs, this entails an uplift of massless integrands to their massive counterparts. Second, utilizing the N=1 superspace formulation of the N=4 sYM and performing algebra of covariant derivatives off-shell. Both techniques provide identical results. These form factors are then studied in the near-mass-shell limit with the off-shellness regularizing emerging infrared divergences. We observe their exponentiation and confirm the octagon anomalous dimension, not the cusp, as the coefficient of the Sudakov double logarithmic behavior. By subtracting these singularities and defining a finite remainder, we verified that its symbol is identical to the one found a decade ago in the conformal case. Beyond-the-symbol contributions are different in the two cases, however., Comment: 24 pages, 6 figures, 1 Mathematica notebook

In this paper, we discuss the factorization of the Sudakov form factor on the Coulomb branch of maximally supersymmetric Yang-Mills theory in the near mass-shell limit. We unravel all pinch singularities of this observable making use of the Method of Regions. We find their operator content in terms of matrix elements of Wilson lines on semi-infinite and finite intervals for the jet and ultrasoft functions, respectively. However, naive factorization into these incoherent momentum components is broken at two-loop order by effects subleading in the parameter of dimensional regularization. To save the day, we perform an appropriate twisting of the functions involved as well as simultaneous finite scheme transformation of the 't Hooft coupling. Infrared physics of twisted jet and ultrasoft functions is governed by the octagon anomalous dimension, while the untwisted ultrasoft function possesses infrared evolution driven by an anomalous dimension different from the ubiquitous cusp., Comment: 36 pages, 6 figures

We consider asymmetric simple exclusion processes with $N$ particles on the one-dimensional discrete torus with $L$ sites with following properties: (i) nearest-neighbor jumps on the torus, (ii) the jump rates depend only on the distance to the next particle in the direction of the jump, (iii) the jump rates are independent of $N$ and $L$. For measures with a long-range two-body interaction potential that depends only on the distance between neighboring particles we prove a relation between the interaction potential and particle jump rates that is necessary and sufficient for the measure to be invariant for the process. The normalization of the measure and the stationary current are computed both for finite $L$ and $N$ and in the thermodynamic limit. For a finitely many particles that evolve on $\mathbb{Z}$ with totally asymmetric jumps it is proved, using reverse duality, that a certain family of nonstationary measures with a microscopic shock and antishock evolves into a convex combination of such measures with weights given by random walk transition probabilities. On macroscopic scale this domain random walk is a travelling wave phenomenon tantamount to phase separation with a stable shock and stable antishock. Various potential applications of this result and open questions are outlined., Comment: 47 pages, 2 figures

We consider a Markovian model for the kinetics of RNA Polymerase (RNAP) which provides a physical explanation for the phenomenon of cooperative pushing during transcription elongation observed in biochemical experiments on Escherichia coli and yeast RNAP. To study how backtracking of RNAP affects cooperative pushing we incorporate into this model backward (upstream) RNAP moves. With a rigorous mathematical treatment of the model we derive conditions on the mutual static and kinetic interactions between RNAP under which backtracking preserves cooperative pushing. This is achieved by exact computation of several key properties in the steady state of this model, including the distribution of headway between two RNAP along the DNA template and the average RNAP velocity and flux.

We study the form factor of the lowest component of the stress-tensor multiplet away from the origin of the moduli space in the spontaneously broken, aka Coulomb, phase of the maximally supersymmetric Yang-Mills theory for decay into three massive W-bosons. The calculations are done at two-loop order by deriving and solving canonical differential equations in the asymptotical limit of nearly vanishing W-masses. We confirm our previous findings that infrared physics of `off-shell observables' is governed by the octagon anomalous dimension rather than the cusp. In addition, the form factor in question possesses a nontrivial remainder function, which was found to be identical to the massless case, upon a proper subtraction of infrared logarithms (and finite terms). However, the iterative structure of the object is more intricate and is not simply related to the previous orders in coupling as opposed to amplitudes/form factors at the origin of the moduli space., Comment: 24 pages, 4 figures, multiple ancillary files

Feynman integral reduction by means of integration-by-parts identities is a major power gadget in a theorist toolbox indispensable for calculation of multiloop quantum effects relevant for particle phenomenology and formal theory alike. An algorithmic approach consists of solving a large sparse non-square system of homogeneous linear equations with polynomial coefficients. While an analytical way of doing this is legitimate and was pursued for decades, it undoubtedly has its limitations when applied in complicated circumstances. Thus, a complementary framework based on modular arithmetic becomes critical on the way to conquer the current `what is possible' frontier. This calls for use of supercomputers to address the reduction problem. In order to properly utilize these computational resources, one has to efficiently optimize the technique for this purpose. Presently, we discuss and implement various methods which allow us to significantly improve performance of Feynman integral reduction within the FIRE environment.

Two-loop multi-leg form factors in off-shell kinematics require knowledge of planar and nonplanar double box Feynman diagrams with massless internal propagators. These are complicated functions of Mandelstam variables and external particle virtualities. The latter serve as regulators of infrared divergences, thus making these observables finite in four space-time dimensions. In this paper, we use the method of canonical differential equations for calculation of (non)planar double box integrals in the near mass-shell kinematical regime, i.e., where virtualities of external particles are much smaller than the Mandelstam variables involved. We deduce a basis of master integrals with uniform transcendental weight based on the analysis of leading singularities by means of the Baikov representation as well as an array of complementary techniques. We dub the former asymptotically canonical since it is valid in the near mass-shell limit of interest. We iteratively solve resulting differential equations up to weight four in terms of multiple polylogarithms., Comment: 17 pages, 1 figure, multiple Mathematica notebooks and ancillary files

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 $\Gamma_{\rm oct}$. 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., Comment: 27 pages, 4 figures

We address the problem of unambiguous reconstruction of rational functions of many variables. This is particularly relevant for recovery of exact expansion coefficients in integration-by-parts identites (IBPs) based on modular arithmetic. These IBPs are indispensable in modern approaches to evaluation of multiloop Feynman integrals by means of differential equations. Modular arithmetic is far more superior to algebraic implementations when one deals with high-multiplicity situations involving a large number of Lorentz invariants. We introduce a new method based on balanced relations which allows one to achieve the goal of a robust functional restoration with minimal data input. The technique is implemented as a Mathematica package Reconstruction.m in the FIRE6 environment and thus successfully demonstrates a proof of concept., Comment: 15 pages, 10 ancillary files with code, scripts and demo; download code @ https://bitbucket.org/feynmanIntegrals/fire/src/master/FIRE6/mm/

We address the problem of evaluation of multiloop Feynman integrals by means of their Mellin-Barnes representation. After a brief overview of available capabilities though open source toolkits and their application in various circumstances, we introduce a new code MBcreate which allows one to automatically deduce a concise Mellin-Barnes representation for a given parametric integral. A thorough discussion of its implementation and use is provided., Comment: 13 pages, 3 ancillary files; download repository @ https://bitbucket.org/feynmanIntegrals/mb/src/master/

We consider the Sudakov form factor in N=4 SYM in the off-shell kinematical regime, which can be achieved by considering the theory on its Coulomb branch. We demonstrate that up two three loops both the infrared-divergent as well as the finite terms do exponentiate, with the coefficient accompanying $\log^2(m^2)$ determined by the octagon anomalous dimension $\Gamma_{oct}$. This behaviour is in strike contrast to previous conjectural accounts in the literature. Together with the finite terms we observe that up to three loops the logarithm of the Sudakov form factor is identical to twice the logarithm of the null octagon $\mathbb{O}_0$, which was recently introduced within the context of integrability-based approaches to four point correlation functions with infinitely-large R-charges. The null octagon $\mathbb{O}_0$ is known in a closed form for all values of the 't Hooft coupling constant and kinematical parameters. We conjecture that the relation between $\mathbb{O}_0$ and the off-shell Sudakov form factor will hold to all loop orders., Comment: 5 pages, 2 figures

It is well-known that on-shell maximally helicity-violating gluon scattering amplitudes in maximally supersymmetric Yang-Mills theory are dual to a bosonic Wilson loop on a null-polygonal contour. The light-like nature of the intervals is a reflection of the mass-shell condition for massless gluons involved in scattering. Presently, we introduce a Wilson loop prototype on a piecewise curvilinear contour that can be interpreted in the T-dual language to correspond to nonvanishing gluon off-shellness. We analyze it first for four sites at one loop and demonstrate that it coincides with the four-gluon amplitude on the Coulomb branch. Encouraged by this fact, we move on to the two-loop order. To simplify our considerations, we only focus on the Sudakov asymptotics of the Wilson loop, when the off-shellness goes to zero. The latter serves as a regulator of short-distance divergences around the perimeter of the loop, i.e., divergences when gluons are integrated over a small vicinity of the Wilson loop cusps. It does not however regulate conventional ultraviolet divergences of interior closed loops. This unavoidably introduces a renormalization scale dependence and thus scheme dependence into the problem. With a choice of the scale setting and a finite renormalization, we observe exponentiation of the double logarithmic scaling of the Wilson loop with the accompanying exponent being given by the so-called hexagon anomalous dimension, which recently made its debut in the origin limit of six-leg gluon amplitudes. This is contrary to the expectation for the octagon anomalous dimension to rather emerge from our analysis, suggesting that the current object encodes physics different from the Coulomb branch scattering amplitudes., Comment: 38 pages, 4 figures; v2: author added, two-loop calculation added, significant text revision

A special class of four-point correlation functions in the maximally supersymmetric Yang-Mills theory is given by the square of the Fredholm determinant of a generalized Bessel kernel. In this note, we re-express its logarithmic derivatives in terms of a two-dimensional Riemann-Hilbert problem. We solve the latter in the null limit making use of the Deift-Zhou steepest descent. We reproduce the exact octagonal anomalous dimension in 't Hooft coupling and provide its novel formulation as a convolution of the non-linear quasiclassical phase with the Fermi distribution in the limit of the infinite chemical potential., Comment: 14 pages, 2 figures

We develop a new technique for computing a class of four-point correlation functions of heavy half-BPS operators in planar N=4 SYM theory which admit factorization into a product of two octagon form factors with an arbitrary bridge length. We show that the octagon can be expressed as the Fredholm determinant of the integrable Bessel operator and demonstrate that this representation is very efficient in finding the octagons both at weak and strong coupling. At weak coupling, in the limit when the four half-BPS operators become null separated in a sequential manner, the octagon obeys the Toda lattice equations and can be found in a closed form. At strong coupling, we exploit the strong Szego limit theorem to derive the leading asymptotic behavior of the octagon and, then, apply the method of differential equations to determine the remaining subleading terms of the strong coupling expansion to any order in the inverse coupling. To achieve this goal, we generalize results available in the literature for the asymptotic behavior of the determinant of the Bessel operator. As a byproduct of our analysis, we formulate a Szego-Akhiezer-Kac formula for the determinant of the Bessel operator with a Fisher-Hartwig singularity and develop a systematic approach to account for subleading power suppressed contributions., Comment: 45 pages, 3 figures; new appendix added with explicit similarity transformation

We present a two-loop calculation of the supersymmetric circular Wilson loop in the N=2* super Yang-Mills theory on the four-sphere. We develop an efficient framework for computing contributing Feynman graphs that relies on using the embedding coordinates combined with the Mellin-Barnes techniques for propagator-like integrals on the sphere. Our results exactly match predictions of supersymmetric localization providing a nontrivial consistency check for the latter in non-conformal settings., Comment: 37 pages, 1 figure

We study a special class of four-point correlation functions of infinitely heavy half-BPS operators in planar N=4 SYM which admit factorization into a product of two octagon form factors. We demonstrate that these functions satisfy a system of nonlinear integro-differential equations which are powerful enough to fully determine their dependence on the 't Hooft coupling and two cross ratios. At weak coupling, solution to these equations yields a known series representation of the octagon in terms of ladder integrals. At strong coupling, we develop a systematic expansion of the octagon in the inverse powers of the coupling constant and calculate accompanying expansion coefficients analytically. We examine the strong coupling expansion of the correlation function in various kinematical regions and observe a perfect agreement both with the expected asymptotic behavior dictated by the OPE and with results of numerical evaluation. We find that, surprisingly enough, the strong coupling expansion is Borel summable. Applying the Borel-Pade summation method, we show that the strong coupling expansion correctly describes the correlation function over a wide region of the 't Hooft coupling., Comment: 43 pages, 5 figures, 2 ancillary files; references updated, typos fixed

ALMA has been operating since 2011, but has not yet been populated with the full suite of intended frequency bands. In particular, ALMA Band 2 (67-90 GHz) is the final band in the original ALMA band definition to be approved for production. We aim to produce a wideband, tuneable, sideband-separating receiver with 28 GHz of instantaneous bandwidth per polarisation operating in the sky frequency range 67-116 GHz. Our design anticipates new ALMA requirements following the recommendations in the 2030 ALMA Development Roadmap. The cryogenic cartridge is designed to be compatible with the ALMA Band 2 cartridge slot, where the coldest components -- the feedhorns, orthomode transducers, and cryogenic low noise amplifiers -- operate at a temperature of 15 K. We use multiple simulation methods and tools to optimise our designs for both the passive optics and the active components. The cryogenic cartridge interfaces with a room temperature cartridge hosting the local oscillator (LO) and the downconverter module. This warm cartridge is largely based on GaAs semiconductor technology and is optimised to match the cryogenic receiver bandwidth with the required instantaneous LO tuning range. Our collaboration has designed, fabricated, and tested multiple technical solutions for each of the components, producing a state-of-the-art receiver covering the full ALMA Band 2 & 3 atmospheric window. The receiver is suitable for deployment on ALMA in the coming years, and is capable of dual-polarisation, sideband-separating observations in intermediate frequency bands spanning 4-18 GHz, for a total of 28 GHz on-sky bandwidth per polarisation channel. We conclude that the 67-116 GHz wideband implementation for ALMA Band 2 is now feasible, and this receiver is a compelling instrumental upgrade that will enhance observational capabilities and scientific reach., Comment: 23 pages, accepted for publication in A&A on 20 Dec 2019. This version corrects the affiliations of 2 co-authors

We consider the so-called simplest correlation function of four infinitely heavy half-BPS operators in planar N=4 SYM in the limit when the operators are light-like separated in a sequential manner. We find a closed-form expression for the correlation function in this limit as a function of the 't Hooft coupling and residual cross ratios. Our analysis heavily relies on the factorization of the correlation function into the product of null octagons and on the recently established determinant representation for the latter. We show that the null octagon is given by a Fredholm determinant of a certain integral operator which has a striking similarity to those previously encountered in the study of two-point correlation functions in exactly solvable models at finite temperature and of level spacing distributions for random matrices. This allows us to compute the null octagon exactly by employing a method of differential equations., Comment: 27 pages, 1 figure; references and discussion updated

We consider a partial light-cone limit of a correlation function of the stress-tensor multiplet and identify an integrable structure emerging at one loop order of perturbation theory. It corresponds to a noncompact open spin chain with one boundary being recoil-less while the other one fully dynamical. We solve the system by means of techniques of the Baxter operator and Separation of Variables. The eigenvalues of separated variables define rapidities of excitations propagating on the color flux tube and encode their factorizable dynamics in the presence of a dynamical boundary., Comment: 22 pages, 8 figures; references added

The Atacama Large Millimeter/sub-millimeter Array (ALMA) is already revolutionising our understanding of the Universe. However, ALMA is not yet equipped with all of its originally planned receiver bands, which will allow it to observe over the full range of frequencies from 35-950 GHz accessible through the Earth's atmosphere. In particular Band 2 (67-90 GHz) has not yet been approved for construction. Recent technological developments in cryogenic monolithic microwave integrated circuit (MMIC) high electron mobility transistor (HEMT) amplifier and orthomode transducer (OMT) design provide an opportunity to extend the originally planned on-sky bandwidth, combining ALMA Bands 2 and 3 into one receiver cartridge covering 67-116 GHz. The IF band definition for the ALMA project took place two decades ago, when 8 GHz of on-sky bandwidth per polarisation channel was an ambitious goal. The new receiver design we present here allows the opportunity to expand ALMA's wideband capabilities, anticipating future upgrades across the entire observatory. Expanding ALMA's instantaneous bandwidth is a high priority, and provides a number of observational advantages, including lower noise in continuum observations, the ability to probe larger portions of an astronomical spectrum for, e.g., widely spaced molecular transitions, and the ability to scan efficiently in frequency space to perform surveys where the redshift or chemical complexity of the object is not known a priori. Wider IF bandwidth also reduces uncertainties in calibration and continuum subtraction that might otherwise compromise science objectives. Here we provide an overview of the component development and overall design for this wideband 67-116 GHz cryogenic receiver cartridge, designed to operate from the Band 2 receiver cartridge slot in the current ALMA front end receiver cryostat., Comment: 8 pages, proceedings from the 8th ESA Workshop on Millimetre-Wave Technology and Applications (https://atpi.eventsair.com/QuickEventWebsitePortal/millimetre-wave/mm-wave)

There is a number of indications that scattering amplitudes in the Aharony-Bergman-Jafferis-Maldacena theory might have a dual description in terms of a holonomy of a supergauge connection on a null polygonal contour in a way analogous to the four-dimensional maximally supersymmetric Yang-Mills theory. However, so far its explicit implementations evaded a successful completion. The difficulty is intimately tied to the lack of the T-self-duality of the sigma model on the string side of the gauge/string correspondence. Unscathed by the last misfortune, we initiate with this study an application of the pentagon paradigm to scattering amplitudes of the theory. With the language being democratic and nondiscriminatory to whether one considers a Wilson loop expectation value or an amplitude, the success in the application of the program points towards a possible unified observable on the field theory side. Our present consideration is focused on two-loop perturbation theory in the planar limit, begging for higher loop data in order to bootstrap current analysis to all orders in the 't Hooft coupling., Comment: 46 pages, 9 figures

We show that non-steric molecular interactions between RNA polymerase (RNAP) motors that move simultaneously on the same DNA track determine strongly the kinetics of transcription elongation. With a focus on the role of collisions and cooperation, we introduce a stochastic model that allows for the exact analytical computation of the stationary properties of transcription elongation as a function of RNAP density, their interaction strength, nucleoside triphosphate concentration, and rate of pyrophosphate release. Cooperative pushing, i.e., an enhancement of the average RNAP velocity and elongation rate, arises due to stochastic pushing. This cooperative effect cannot be explained by steric hindrance alone but requires a sufficiently strong molecular repulsion. It disappears beyond a critical RNAP density, above which jamming due to collisions takes over. For strong stochastic blocking the cooperative pushing is suppressed at low RNAP densities, but a reappears at higher densities., Comment: 26 pages, 6 figures

Context: We describe the new SEPIA (Swedish-ESO PI Instrument for APEX) receiver, which was designed and built by the Group for Advanced Receiver Development (GARD), at Onsala Space Observatory (OSO) in collaboration with ESO. It was installed and commissioned at the APEX telescope during 2015 with an ALMA Band 5 receiver channel and updated with a new frequency channel (ALMA Band 9) in February 2016. Aims: This manuscript aims to provide, for observers who use the SEPIA receiver, a reference in terms of the hardware description, optics and performance as well as the commissioning results. Methods: Out of three available receiver cartridge positions in SEPIA, the two current frequency channels, corresponding to ALMA Band 5, the RF band 158--211 GHz, and Band 9, the RF band 600--722 GHz, provide state-of-the-art dual polarization receivers. The Band 5 frequency channel uses 2SB SIS mixers with an average SSB noise temperature around 45K with IF (intermediate frequency) band 4--8 GHz for each sideband providing total 4x4 GHz IF band. The Band 9 frequency channel uses DSB SIS mixers with a noise temperature of 75--125K with IF band 4--12 GHz for each polarization. Results: Both current SEPIA receiver channels are available to all APEX observers., Comment: Accepted for publication in Astronomy & Astrophysics

By performing resummation of small fermion-antifermion pairs within the pentagon form factor program to scattering amplitudes in planar N = 4 superYang-Mills theory, we construct multichannel conformal blocks within the flux-tube picture for N-sided NMHV polygons. This procedure is equivalent to summation of descendants of conformal primaries in the OPE framework. The resulting conformal partial waves are determined by multivariable hypergeometric series of Lauricella-Saran type., Comment: 11 pages, 1 figure

The form factor program for the regularized space-time S-matrix in planar maximally supersymmetric gauge theory, known as the pentagon operator product expansion, is formulated in terms of flux-tube excitations propagating on a dual two-dimensional world-sheet, whose dynamics is known exactly as a function of 't Hooft coupling. Both MHV and non-MHV amplitudes are described in a uniform, systematic fashion within this framework, with the difference between the two encoded in coupling-dependent helicity form factors expressed via Zhukowski variables. The nontrivial SU(4) tensor structure of flux-tube transitions is coupling independent and is known for any number of charged excitations from solutions of a system of Watson and Mirror equations. This description allows one to resum the infinite series of form factors and recover the space-time S-matrix exactly in kinematical variables at a given order of perturbation series. Recently, this was done for the hexagon. Presently, we successfully perform resummation for the seven-leg tree NMHV amplitude. To this end, we construct the flux-tube integrands of the fifteen independent Grassmann component of the heptagon with an infinite number of small fermion-antifermion pairs accounted for in NMHV two-channel conformal blocks., Comment: 23 pages, 3 figures; typos fixed

Twist fields were introduced a few decades ago as a quantum counterpart to classical kink configurations and disorder variables in low dimensional field theories. In recent years they received a new incarnation within the framework of geometric entropy and strong coupling limit of four-dimensional scattering amplitudes. In this paper, we study their two-point correlation functions in a free massless scalar theory, namely, twist--twist and twist--anti-twist correlators. In spite of the simplicity of the model in question, the properties of the latter are far from being trivial. The problem is reduced, within the formalism of the path integral, to the study of spectral determinants on surfaces with conical points, which are then computed exactly making use of the zeta function regularization. We also provide an insight into twist correlators for a massive complex scalar by means of the Lifshitz-Krein trace formula., Comment: 21 pages, 2 figures

Twist fields emerge in a number of physical applications ranging from entanglement entropy to scattering amplitudes in four-dimensional gauge theories. In this work, their vacuum expectation values are studied in the path integral framework. By performing a gauge transformation, their correlation functions are reduced to field theory of matter fields in external Aharonov-Bohm vortices. The resulting functional determinants are then analyzed within the zeta function regularization for the spectrum of Bessel zeros and concise formulas are derived., Comment: 11 pages, 1 figure

The near-collinear expansion of scattering amplitudes in maximally supersymmetric Yang-Mills theory at strong coupling is governed by the dynamics of stings propagating on the five sphere. The pentagon transitions in the operator product expansion which systematize the series get reformulated in terms of matrix elements of branch-point twist operators in the two-dimensional O(6) nonlinear sigma model. The facts that the latter is an asymptotically free field theory and that there exists no local realization of twist fields prevents one from explicit calculation of their scaling dimensions and operator product expansion coefficients. This complication is bypassed making use of the equivalence of the sigma model to the infinite-level limit of WZNW models perturbed by current-current interactions, such that one can use conformal symmetry and conformal perturbation theory for systematic calculations. Presently, to set up the formalism, we consider the O(3) sigma model which is reformulated as perturbed parafermions., Comment: 16 pages, 4 figures