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Linear confinement with Casimir scaling of the string tension in confining gauge theories is a consequence of a certain property of the Polyakov loop related to random matrices. This mechanism does not depend on the details of the theories (neither the gauge group nor dimensions) and explains approximate Casimir scaling below string-breaking length. In this paper, we study 3d SU(2) pure Yang-Mills theory numerically and find the same random-matrix behavior for rectangular Wilson loops. We conjecture that this is a universal feature of strongly coupled confining gauge theories. [ABSTRACT FROM AUTHOR]

In this paper, we consider the Hamiltonian analysis of Yang–Mills theory and some variants of it in three space–time dimensions using the Schrödinger representation. This representation, although technically more involved than the usual covariant formulation, may be better suited for some nonperturbative issues. Specifically for the Yang–Mills theory, we explain how to set up the Hamiltonian formulation in terms of manifestly gauge-invariant variables and set up an expansion scheme for solving the Schrödinger equation. We review the calculation of the string tension, the Casimir energy and the propagator mass and compare with the results from lattice simulations. The computation of the first set of corrections to the string tension, string breaking effects, extensions to the Yang–Mills–Chern–Simons theory and to the supersymmetric cases are also discussed. We also comment on how entanglement for the vacuum state can be formulated in terms of the BFK gluing formula. This paper concludes with a discussion of the status and prospects of this approach. [ABSTRACT FROM AUTHOR]

We study 4-dimensional SU(N) gauge theory with one adjoint Weyl fermion and fundamental matter — either bosonic or fermionic. Symmetries, their 't Hooft anomalies, and the Vafa-Witten-Weingarten theorems strongly constrain the possible bulk phases. The first part of the paper is dedicated to a single fundamental fermion or boson. As long as the adjoint Weyl fermion is massless, this theory always possesses a ℤ 2 N χ chiral symmetry, which breaks spontaneously, supporting N vacua and domain walls between them for a generic mass of the matter fields. We argue, however, that the domain walls generically undergo a phase transition, and we establish the corresponding 3d gauge theories on the walls. The rest of the paper is dedicated to studying the multi-flavor fundamental matter. Here, the phases crucially depend on the ratio of the number of colors and the number of fundamental flavors. We also discuss the limiting scenarios of heavy adjoint and fundamentals, which align neatly with our current understanding of QCD and N = 1 super Yang-Mills theory. [ABSTRACT FROM AUTHOR]

We study the meson spectrum of the N = 4 supersymmetric Yang-Mills theory with N = 2 fundamental hypermultiplets for a finite electric field by using the D3/D7 model. The spectrum for scalar and vector mesons is computed by analyzing the (quasi-)normal modes for the fluctuations of the D7-brane embedding and gauge fields. In the presence of an electric field, two different phases in the background are realized: the meson and dissociation phases. In this paper, we analyze the meson spectrum of scalar and vector mesons for all ranges of the electric field and explore the effect of the electric field on the meson spectrum, that is, the Stark effect. In the meson spectrum, we observe the avoided crossing between different levels due to the coupling of fluctuations via the electric field. [ABSTRACT FROM AUTHOR]

This paper is concerned with the Cauchy problem for an energy-supercritical nonlinear wave equation in odd space dimensions that arises in equivariant Yang-Mills theory. In each dimension, there is a self-similar finite-time blowup solution to this equation known in closed form. It will be proved that this profile is stable in the whole space under small perturbations of the initial data. The blowup analysis is based on a recently developed coordinate system called hyperboloidal similarity coordinates and depends crucially on growth estimates for the free wave evolution, which will be constructed systematically for odd space dimensions in the first part of this paper. This allows to develop a nonlinear stability theory beyond the singularity. [ABSTRACT FROM AUTHOR]

In this paper, we consider Einstein–Hilbert gravity in the presence of cosmological constant and an electric field of Yang–Mills type, which is minimally coupled to gravity. We couple the Ricci scalar to the Yang–Mills invariant to obtain a modified theory of gravity. The black brane solution of this model is introduced up to the first order of the R F μ α (a) F (a) μ α term. Then, the color non-Abelian direct current (DC) conductivity and the ratio of shear viscosity to entropy density are calculated for this solution. Our results recover the Yang–Mills Schwarzschild AdS black brane in the limit of q 2 → 0. [ABSTRACT FROM AUTHOR]

We consider the gauge/gravity correspondence between maximally supersymmetric Yang–Mills theory in (p + 1) dimensions and superstring theory on the near-horizon limit of the D p -brane solution. The string-frame metric is AdS p + 2 × S 8 − p times a Weyl factor, and there is no conformal symmetry except for p = 3. In a previous paper by one of the present authors, the free-field result of gauge theory has been reproduced from string theory for a particular operator that has angular momentum along S 8 − p . In this paper, we extend this result to operators that have angular momenta along AdS p + 2. Our approach is based on a Euclidean formulation proposed by Dobashi et al. [Nucl. Phys. B 665 , 94 (2003)] and on the "string bit" picture. We first show that the spinning string solution in Lorentzian AdS, found by Gubser et al. [Nucl. Phys. B 636 , 99 (2002)], can be recast in a form that connects two points on the boundary of Euclidean AdS. The transition amplitudes of such strings can be interpreted as gauge theory correlators. We study the case of zero gauge coupling by ignoring interactions among string bits (massless particles in 10D spacetime that constitute a string), and show that the free-field results of gauge theory are reproduced. [ABSTRACT FROM AUTHOR]

In this paper, we investigate two types of U(1)-gauge field theories on G 2 -manifolds. One is the U(1)-Yang–Mills theory which admits the classical instanton solutions. We show that G 2 -manifolds emerge from the anti-self-dual U(1) instantons, which is an analogy of Yang's result for Calabi–Yau manifolds. The other one is the higher-order U(1)-Chern–Simons theory as a generalization of Kähler–Chern–Simons theory. We introduce the notion of higher-order U(1)-instanton, as the vacuum configurations of higher-order U(1)-Chern–Simons theory. By suitable choice of gauge and regularization technique, we calculate the partition function under semiclassical approximation. Finally, to make sure of the invariance at quantum level under the large gauge transformations, we use Deligne–Beilinson cohomology theory to give the higher-order U(1)-Chern–Simons actions (U(1)-BF-type actions) for nontrivial U(1)-principle bundles. [ABSTRACT FROM AUTHOR]

Krylov complexity has been proposed as a diagnostic of chaos in non-integrable lattice and quantum mechanical systems, and if the system is chaotic, Krylov complexity grows exponentially with time. However, when Krylov complexity is applied to quantum field theories, even in free theory, it grows exponentially with time. This exponential growth in free theory is simply due to continuous momentum in non-compact space and has nothing to do with the mass spectrum of theories. Thus by compactifying space sufficiently, exponential growth of Krylov complexity due to continuous momentum can be avoided. In this paper, we propose that the Krylov complexity of operators such as O = Tr[FμνFμν] can be an order parameter of confinement/deconfinement transitions in large N quantum field theories on such a compactified space. We explicitly give a prescription of the compactification at finite temperature to distinguish the continuity of spectrum due to momentum and mass spectrum. We then calculate the Krylov complexity of N = 4, 0 SU(N) Yang-Mills theories in the large N limit by using holographic analysis of the spectrum and show that the behavior of Krylov complexity reflects the confinement/deconfinement phase transitions through the continuity of mass spectrum. [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 relationship between gauge and gravity amounts to understanding the underlying new geometrical local structures. These structures are new tetrads specially devised for Yang-Mills theories, Abelian and non-Abelian in four-dimensional Lorentzian curved spacetimes. In the present paper, a new tetrad is introduced for the Yang-Mills formulation. These new tetrads establish a link between local groups of gauge transformations and local groups of spacetime transformations that we previously called LB1 and LB2. New theorems are proved regarding isomorphisms between local internal groups and local tensor products of spacetime LB1 and LB2 groups of transformations. These new tetrads define at every point in spacetime two orthogonal planes that we called blades or planes one and two. These are the local planes of covariant diagonalization of the stress-energy tensor. These tetrads are gauge dependent. Tetrad local gauge transformations leave the tetrads inside the local original planes without leaving them. These local tetrad gauge transformations enable the possibility to connect local gauge groups Abelian or non-Abelian with local groups of tetrad transformations. On the local plane one, the Abelian group of gauge transformations was already proved to be isomorphic to the tetrad local group of transformations LB1, for example. LB1 is plus two different kinds of discrete transformations. On the local orthogonal plane two is isomorphic to LB2 which is just . That is, we proved that LB1 is isomorphic to which is a remarkable result since a noncompact group plus two discrete transformations is isomorphic to a compact group. These new tetrads have displayed manifestly and nontrivially the coupling between Yang-Mills fields and gravity. The new tetrads and the stress-energy tensor allow for the introduction of three new local gauge invariant objects. Using these new gauge invariant objects and in addition a new general local duality transformation, a new algorithm for the gauge invariant diagonalization of the Yang-Mills stress-energy tensor is developed as an application. This is a paper about grand Standard Model gauge theories - General Relativity gravity unification and grand group unification in four-dimensional curved Lorentzian spacetimes. [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 short paper gives a brief overview of the manifestly covariant canonical gauge gravity (CCGG) that is rooted in the De Donder‐Weyl Hamiltonian formulation of relativistic field theories, and the proven methodology of the canonical transformation theory. That framework derives, from a few basic physical and mathematical assumptions, equations describing generic matter and gravity dynamics with the spin connection emerging as a Yang Mills‐type gauge field. While the interaction of any matter field with spacetime is fixed just by the transformation property of that field, a concrete gravity ansatz is introduced by the choice of the free (kinetic) gravity Hamiltonian. The key elements of this approach are discussed and its implications for particle dynamics and cosmology are presented. New insights: Anomalous Pauli coupling of spinors to curvature and torsion of spacetime, spacetime with (A)dS ground state, inertia, torsion and geometrical vacuum energy, Zero‐energy balance of the Universe leading to a vanishing cosmological constant and torsional dark energy. [ABSTRACT FROM AUTHOR]

Effective String Theory (EST) represents a powerful non-perturbative approach to describe confinement in Yang-Mills theory that models the confining flux tube as a thin vibrating string. EST calculations are usually performed using the zeta-function regularization: however there are situations (for instance the study of the shape of the flux tube or of the higher order corrections beyond the Nambu-Goto EST) which involve observables that are too complex to be addressed in this way. In this paper we propose a numerical approach based on recent advances in machine learning methods to circumvent this problem. Using as a laboratory the Nambu-Goto string, we show that by using a new class of deep generative models called Continuous Normalizing Flows it is possible to obtain reliable numerical estimates of EST predictions. [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]

Similar to gravity, an infinite tower of symmetries generated by higher-spin charges has been identified in Yang-Mills theory by studying collinear limits or celestial operator products of gluons. This work aims to recover this loop symmetry in terms of charge aspects constructed on the gluonic Fock space. We propose an explicit construction for these higher spin charge aspects as operators which are polynomial in the gluonic annihilation and creation operators. The core of the paper consists of a proof that the charges we propose form a closed loop algebra to quadratic order. This closure involves using the commutator of the cubic order expansion of the charges with the linear (soft) charge. Quite remarkably, this shows that this infinite-dimensional symmetry constrains the non-linear structure of Yang-Mills theory. We provide a similar all spin proof in gravity for the so-called global quadratic (hard) charges which form the loop wedge subalgebra of w1+∞. [ABSTRACT FROM AUTHOR]

In the search of Yang-Mills (YM) instanton sheaves with topological charge two, the rank of β matrix in the monad construction can be dropped from the bundle case with rank β=2 to either rank β=1 [S. H. Lai, J. C. Lee and I. H. Tsai, Yang-Mills instanton sheaves, Ann. Phys.377 (2017) 446] or 0 on some points of CP³ of the sheaf cases. In this paper, we first show that the sheaf case with rank β=0 does not exist for the previous construction of SU(2) complex YM instantons [S. H. Lai, J. C. Lee and I. H. Tsai, Biquaternions and ADHM construction of concompact SL(2,C) Yang-Mills instantons, Ann. Phys.361 (2015) 14]. We then show that in the new "extended complex YM instantons" discovered in this paper, rank β can be either 2 on the whole CP³ (bundle) with some given ADHM data or 1, 0 on some points of CP³ with other ADHM data (sheaves). These extended SU(2) complex YM instantons have no real instanton counterparts. Finally, the potential applications to real physics systems are noted in the end of the paper. [ABSTRACT FROM AUTHOR]

The gauge formalism in telepalallel gravity provides an interesting viewpoint to describe interactions according to an anholonomic observer's tetrad basis. Without going into assessing the complete viability of quantization in an early stage, this paper explores classical gravity within the framework of a classical-to-quantum bridge between the SU(1, 3) Yang–Mills gauge formalism and the gauge-like treatment of teleparallel gravity. Specifically, the perturbed spacetime algebra with Weitzenböck connection can be assimilated to a local complexification based on the SU(1, 3) Yang–Mills theory, what we call hypercolor or, simply, color. The formulation of the hypercolor dynamics is build by a translational gauge, as in the teleparallel gravities. In particular, this work analyses small perturbations of a metric decomposition related to the Wilson line and the Kaluza–Klein metric, but obtaining electrodynamics in four dimensions. The spacetime coordinates are now matrices that represent elements of the su (1 , 3) algebra. To make compatible the formulation of a colored gravity with the Lorentz force and the Maxwell equations, it is enough to define every energy potential origin as 0 in the event horizon instead of the classic zero potential at infinity. Under the colored gravity framework, standard electromagnetism can be obtained as a particular abelian case. [ABSTRACT FROM AUTHOR]

It was recently argued by Nguyen, Tanizaki and Ünsal that two-dimensional pure Yang–Mills theory is equivalent to (decomposes into) a disjoint union of (invertible) quantum field theories, known as universes. In this paper, we compare this decomposition to the Gross–Taylor expansion of two-dimensional pure S U (N) Yang–Mills theory in the large- N limit as the string field theory of a sigma model. Specifically, we study the Gross–Taylor expansion of individual Nguyen–Tanizaki–Ünsal universes. These differ from the Gross–Taylor expansion of the full Yang–Mills theory in two ways: a restriction to single instanton degrees, and some additional contributions not present in the expansion of the full Yang–Mills theory. We propose to interpret the restriction to single instanton degrees as implying a constraint, namely that the Gross–Taylor string has a global (higher-form) symmetry with Noether current related to the worldsheet instanton number. We compare two-dimensional pure Maxwell theory as a prototype obeying such a constraint, and also discuss in that case an analogue of the Witten effect arising under two-dimensional theta angle rotation. We also propose a geometric interpretation of the additional terms, in the special case of Yang–Mills theories on 2-spheres. In addition, also for the case of theories on 2-spheres, we propose a reinterpretation of the terms in the Gross–Taylor expansion of the Nguyen–Tanizaki–Ünsal universes, replacing sigma models on branched covers by counting disjoint unions of stacky copies of the target Riemann surface, that makes the Nguyen–Tanizaki–Ünsal decomposition into invertible field theories more nearly manifest. As the Gross–Taylor string is a sigma model coupled to worldsheet gravity, we also briefly outline the tangentially related topic of decomposition in two-dimensional theories coupled to gravity. [ABSTRACT FROM AUTHOR]

In this paper, we study the holographic dual to an asymptotically anti-de Sitter black brane in an Einstein–Yang–Mills model with a non-minimal coupling between the Riemann and Yang–Mills fields. First, we construct a planar black hole solution of this model up to the first order of the non-minimal coupling of the Yang–Mills field with the Riemann–Christoffel tensor, denoted as q 2. Then, we calculate the color non-abelian direct current conductivity and the ratio of shear viscosity to entropy density for this solution. Our result for the shear viscosity η to entropy density s ratio saturates the Kovtun, Son, and Starinets bound, which is proportional to 1 4 π . However, our result for the conductivity is new up to the first order of q 2. [ABSTRACT FROM AUTHOR]

This paper describes the experimental investigation and numerical simulation of a novel electromechanical milling principle: the direct transformation of energy into the movement of milling beads with special magnetic properties. The experimental results show that this principle is ideally suited for the finest grinding of organic agents. Anthraquinone particles with a median size of 25.5 µm were electromechanically ground to 1 µm and the magnetic field strength in the process chamber has the greatest influence on milling results. The developed model reveals that the distribution of the time‐ and location‐dependent vector gradient of the magnetic field in the process chamber determines the energy transfer from the exciter systems to the milling beads and hence the grinding results. With a suitable characterization of the vector gradient distribution, it is possible to establish a correlation between the vector gradient and specific milling beads power. This correlation is fundamental for the design of electromechanical milling machines. [ABSTRACT FROM AUTHOR]

In this paper we consider perturbation theory in generic two-dimensional sigma models in the so-called first-order formalism, using the coordinate regularization approach. Our goal is to analyze the first-order formalism in application to β functions and compare its results with the standard geometric calculations. Already in the second loop, we observe deviations from the geometric results that cannot be explained by the regularization/renormalization scheme choices. Moreover, in certain cases the first-order calculations produce results that are not symmetric under the classical diffeomorphisms of the target space. Although we could not present the full solution to this remarkable phenomenon, we found some indirect arguments indicating that an anomaly similar to that established in supersymmetric Yang-Mills theory might manifest itself starting from the second loop. We discuss why the difference between two answers might be an infrared effect, similar to that in β functions in supersymmetric Yang-Mills theories. In addition to the generic Kähler target spaces we discuss in detail the so-called Lie-algebraic sigma models. In particular, this is the case when the perturbed field G i j ¯ is a product of the holomorphic and antiholomorphic currents satisfying two-dimensional current algebra. [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]

In this paper we study two-loop calculations in the Yang–Mills theory. Using the heat kernel method we construct two Green functions and add contributions to them, corresponding to the zero modes of the Laplace operator. We show by the direct calculations that such additions do not affect the second coefficient of the β-function in the Yang–Mills theory. [ABSTRACT FROM AUTHOR]

It is well-known that the general Manakov system is a 2-components nonlinear Schrödinger equation with 4 nonzero real parameters. The analytic property of the general Manakov system has been well-understood though it looks complicated. This paper devotes to exploring geometric properties of this system via the prescribed curvature representation in the category of Yang-Mills' theory. Three models of moving curves evolving in the symmetric Lie algebras u(2,1) = kα ⊕ mα (α = 1, 2) and u(3) = k3 ⊕ m3 are shown to be simultaneously the geometric realization of the general Manakov system. This reflects a new phenomenon in geometric realization of a partial differential equation/system. [ABSTRACT FROM AUTHOR]

In this work we obtain the planar free energy for the Hermitian one-matrix model with various choices of the potential. We accomplish this by applying an approach that bypasses the usual diagonalization of the matrices and the introduction of the eigenvalue density, to directly zero in the evaluation of the planar free energy. In the first part of the paper, we focus on potentials with finitely many terms. For various choices of potentials, we manage to find closed expressions for the planar free energy, and in some cases determine or bound their radius of convergence as a series in the 't Hooft coupling. In the second part of the paper we consider specific examples of potentials with infinitely many terms, that arise in the study of N = 2 super Yang-Mills theories on S4, via supersymmetric localization. In particular, we manage to write the planar free energy of two non-conformal examples: SU(N) with Nf < 2N, and N = 2*. [ABSTRACT FROM AUTHOR]

In this short note, we will prove in a few steps that the new tetrads introduced previously in Einstein–Maxwell–Yang–Mills four-dimensional Lorentzian spacetimes where gravitational and Yang–Mills fields are present contain both the necessary information to provide the gravitational field and the necessary information to provide the electromagnetic and Yang–Mills fields as well. These new tools thus become grand unification objects. [ABSTRACT FROM AUTHOR]

This paper provides an existence and uniqueness result for the viscosity solution of the relativistic inhomogeneous Vlasov equation with a given Yang-Mills field in temporal jauge. The geometric background used here is the Schwarzschild outer space-time. [ABSTRACT FROM AUTHOR]

We recently proved that, when integrating out the spacetime dependence with a certain integration measure, four-point correlators O 2 O 2 O p i O p i in 풩 = 4 supersymmetric Yang-Mills theory with SU(N) gauge group are governed by a universal Laplace-difference equation. Here O p i is a superconformal primary with charge p and degeneracy i. These physical observables, called integrated correlators, are modular-invariant functions of Yang-Mills coupling τ. The Laplace-difference equation is a recursion relation that relates integrated correlators of operators with different charges. In this paper, we introduce the generating functions for these integrated correlators that sum over the charge. By utilising the Laplace-difference equation, we determine the generating functions for all the integrated correlators, in terms of the initial data of the recursion relation. We show that the transseries of the integrated correlators in the large-p (i.e. large-charge) expansion for a fixed N consists of three parts: 1) is independent of τ, which behaves as a power series in 1/p, plus an additional log(p) term when i = j; 2) is a power series in 1/p, with coefficients given by a sum of the non-holomorphic Eisenstein series; 3) is a sum of exponentially decayed modular functions in the large-p limit, which can be viewed as a generalisation of the non-holomorphic Eisenstein series. When i = j, there is an additional modular function of τ that is independent of p and is fully determined in terms of the integrated correlator with p = 2. The Laplace-difference equation was obtained with a reorganisation of the operators that means the large-charge limit is taken in a particular way here. From these SL(2, ℤ)-invariant results, we also determine the generalised 't Hooft genus expansion and the associated large-p non-perturbative corrections of the integrated correlators by introducing λ = p g YM 2 . The generating functions have subtle differences between even and odd N, which have important consequences in the large-charge expansion and resurgence analysis. We also consider the generating functions of the integrated correlators for some fixed p by summing over N, and we study their large-N behaviour, as well as comment on the similarities and differences between the large-p expansion and the large-N expansion. [ABSTRACT FROM AUTHOR]

The existence of interacting higher-spin theories is tightly constrained by many no-go theorems. In this paper, we construct a chiral, higher-spin generalization of Yang–Mills theory in flat space which avoids these no-go theorems and has non-trivial tree-level scattering amplitudes with some higher-spin external legs. The fields and action are complex, so the theory is non-unitary and parity-violating, yet we find surprisingly compact formulae for all-multiplicity tree-level scattering amplitudes in the maximal helicity violating (MHV) sector, where the two negative helicity particles have identical but arbitrary spin. This is possible because the theory admits a perturbative expansion around its self-dual sector. Using twistor theory, we prove the classical integrability of this self-dual sector and show that it can be described on spacetime by an infinite tower of interacting massless scalar fields. We also give a twistor construction of the full theory and use it to derive the formula for the MHV amplitude. [ABSTRACT FROM AUTHOR]

As known, the realistic, exponential, fall-off of the rate of production of light mesons in the chromo-electric field of a quark–antiquark string, as a function of the meson mass, can be obtained from the Schwinger-formula Gaussian fall-off within a phenomenological approach which assumes a certain distribution of the string tension. This approach gets a clear meaning in the London limit of the dual superconductor, where the logarithmic increase of the chromo-electric field towards the core of the string leads precisely to the change of the Gaussian fall-off to the exponential one, thus allowing for an identification of the phenomenological distribution of the string tension. In this paper, we demonstrate that, for this distribution of the string tension, the distribution of large-size Yang–Mills instantons, which are interacting with the confining monopole background, becomes O (1 / ρ 3) , where ρ is the size of an instanton. Since such a distribution of large-size instantons is known to yield confinement, we conclude that, in the London limit of the dual-superconductor vacuum, instantons can form a confining medium, and we evaluate their contribution to the total string tension. [ABSTRACT FROM AUTHOR]

In this paper, we propose a generalization of the improved gauge unfixing formalism in order to generate gauge symmetries in the non-Abelian valued systems. This generalization displays a proper and formal reformulation of second-class systems within the phase space itself. Then, we present our formalism in a manifestly gauge invariant resolution of the SU(N) massive Yang-Mills and SU(2) Skyrme models, where gauge invariant variables are derived. [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 this paper, we study the Maxwell equations in the domain of outer-communication of the Schwarzschild black hole. We prove that if the middle components of the non-stationary solutions of the Maxwell equations verify a Morawetz-type estimate supported on a compact region in space around the trapped surface, then the components of the Maxwell fields decay uniformly in the entire exterior of the Schwarzschild black hole, including the event horizon. This is shown by making only use of Sobolev inequalities combined with energy estimates using the Maxwell equations directly. The proof does not pass through the scalar wave equation on the Schwarzschild black hole, does not need to decouple the middle components for the Maxwell fields, and would be in particular useful for the non-abelian case of the Yang–Mills equations where the decoupling of the middle components cannot occur. In fact, the estimates for the hereby argument are still valid for the Yang–Mills fields except for the Lie derivatives of the fields that are involved in the proof. [ABSTRACT FROM AUTHOR]

We propose a proper definition of the vacuum expectation value of the stress energy tensor 〈0| Tμν| 0〉 for integrable quantum field theories in two spacetime dimensions, which is the analog of the cosmological constant in 4d. For a wide variety of models, massive or massless, we show ρ vac = − m 2 / 2 g exactly, where g is a generalized coupling which we compute and m is a basic mass scale. The kinds of models we consider are the massive sinh-Gordon and sine-Gordon theories and perturbations of the Yang-Lee and 3-state Potts models, pure T T ¯ perturbations of infra-red QFT's, and UV completions of the latter which are massless flows between UV and IR fixed points. In the massive case m is the physical mass of the lightest particle and g is related to parameters in the 2-body S-matrix. In some examples ρvac = 0 due to a fractional supersymmetry. For massless cases, m can be a scale of spontaneous symmetry breaking. The "cosmological constant problem" generically arises in the free field limit g → 0, thus interactions can potentially resolve the problem at least for most cases considered in this paper. We speculate on extensions of these results to 4 spacetime dimensions and propose ρ vac = m 4 / 2 g , however without integrability we cannot yet propose a precise manner in which to calculate g . Nevertheless, based on cosmological data on ρvac, if g ~ 1 then it is worth pointing out that the lightest mass particle is on the order of experimental values of proposed neutrino masses. [ABSTRACT FROM AUTHOR]

We advance the exploration of cluster-algebraic patterns in the building blocks of scattering amplitudes in N = 4 super Yang-Mills theory. In particular, we conjecture that, given a maximal cut of a loop amplitude, Landau singularities and poles of each Yangian invariant appearing in any representation of the corresponding leading singularities can be found together in a cluster. We check these adjacencies for all one-loop amplitudes up to 9 points. Along the way, we also prove that all (rational) N²MHV Yangian invariants are cluster adjacent, confirming original conjectures. [ABSTRACT FROM AUTHOR]

In this paper, we take into account the Gribov copies present in 3D Yang–Mills–Higgs theory with a constant vector background whose presence breaks the Lorentz symmetry. The constant vector background is introduced within the non-Abelian aether term. Here, we show that this term arises as a one-loop correction. The influence of the aether coupling constant on the system is treated afterwards. As a result, we find that for some values of it the theory can be driven from a nonperturbative regime to a perturbative one. In this paper, we work with the Higgs field in the fundamental representation and in the Landau gauge. [ABSTRACT FROM AUTHOR]

A high-energy ball mill, such as a planetary ball mill, is widely used for preparing a homogeneously mixed powder and reducing particle size. Because of the high impact energy generated by the collision of ball media, the planetary ball milling is expected to produce local high-temperature and high-pressure zones. In wet milling, the solubility of the material varies owing to the local and instantaneous changes caused by the collision. Consequently, mechanochemical reactions through a dissolution–precipitation mechanism can be attained without external heating. In this paper, we show the wet mechanochemical process in water to synthesize functional hydrous or hydrate materials with various shapes, including nanosheets, nanotubes, plates, flakes, rods, and nanoparticles. Morphology-controlled particles can be obtained by only adjusting the milling conditions, such as milling time, ball size, and centrifugal acceleration. Further, the products can be converted into electrode materials for Li-ion batteries, retaining the precursor morphologies. This wet mechanochemical synthesis can be also applied in a bead mill, where mass production and continuous processing are possible. The wet mechanochemical process is a new particle synthesis method that can achieve both grinding and crystal growth. [ABSTRACT FROM AUTHOR]

We construct local solutions to the Yang–Mills heat flow (in the DeTurck gauge) for a certain class of random distributional initial data, which includes the 3D Gaussian free field. The main idea, which goes back to work of Bourgain as well as work of Da Prato–Debussche, is to decompose the solution into a rougher linear part and a smoother nonlinear part, and to control the latter by probabilistic arguments. In a companion work, we use the main results of this paper to propose a way toward the construction of 3D Yang–Mills measures. [ABSTRACT FROM AUTHOR]

In this paper, provide a survey of recent studies of supergroup gauge theory. We first discuss the supermatrix model as a zero-dimensional toy model of supergroup gauge theory and its geometric and algebraic characterization. We then focus on four-dimensional Yang–Mills theory with supergroup gauge symmetry and explore its nonperturbative properties, including instanton calculus, Seiberg–Witten geometry, Bethe/gauge correspondence, and its realization with intersecting defects. [ABSTRACT FROM AUTHOR]

In the previous paper, we have shown the existence of magnetic monopoles in the pure SU(2) Yang–Mills theory with a gauge-invariant mass term for the gluon field being introduced. In this paper, we extend our previous construction of magnetic monopoles to obtain dyons with both magnetic and electric charges. In fact, we solve under the static and spherically symmetric ansatz the field equations of the SU(2) "complementary" gauge-scalar model, which is the SU(2) Yang–Mills theory coupled to a single adjoint scalar field whose radial degree of freedom is eliminated. We show that the novel dyon solution can be identified with the gauge field configuration of a dyon with a minimum magnetic charge in the massive Yang–Mills theory. Moreover, we compare the dyon of the massive Yang–Mills theory obtained in this way with the Julia–Zee dyon in the Georgi–Glashow gauge-Higgs scalar model and the dyonic extension of the Wu–Yang magnetic monopole in the pure Yang–Mills theory. Finally, we identify the novel dyon solution found in this paper with a dyon configuration on S 1 × R 3 space with nontrivial holonomy and propose to use it to understand the confinement/deconfinement phase transition in the Yang–Mills theory at finite temperature, instead of using the dyons constituting the Kraan–van Baal–Lee–Lu caloron. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the interaction of non-Abelian SU(2) Yang–Mills progressive waves with gravitational waves. We solve and obtain some interesting solutions to pure Yang–Mills equations in different backgrounds, and perturbative solutions induced due to gravitational waves. These perturbations show 'beat patterns' and depending on boundary conditions, changes in frequency. In flat space-time, when the Yang–Mills fields and the gravitational waves are in the same direction there is no interaction, unless there is self interaction of the Yang–Mills fields. In the system with non-zero self interaction the amplitudes of the perturbation are inversely proportional to the Yang–Mills coupling constant. In a cosmological background, the Yang–Mills fields and the gravitational wave interact when they are in the same direction even without self interaction of the Yang–Mills progressive fields. We find that in the electroweak symmetry broken phase of the gauge fields, the interactions are perturbative only for an infinitesimal time. [ABSTRACT FROM AUTHOR]

Soft magnetic composites (SMCs) need a stable matrix to apply heat treatments for enhancing their magnetic characteristics. A stable matrix can be offered by alumina, but the densification of the ferromagnetic particles covered by this oxide (by sintering) can be very difficult. This paper proposes a feasible synthesis route for obtaining alumina matrix SMCs. An Fe-Si-Al alloy with nominal composition Fe85Si9Al6 was obtained by mechanical alloying of elemental Fe, Si, and Al powders, and further, the as-milled powders were superficially oxidized by immersion in HCl solution. The oxide layer was composed of iron, silicon, and aluminum oxides, as the Fourier-transform infrared spectroscopy technique revealed. The Fe-Si-Al@oxide powder was densified by the spark plasma sintering technique—SPS. Upon sintering, a continuous matrix of oxide (mainly alumina) was formed by the reaction of the Fe-Si-Al powder coreswith their oxide layer. The main part of the composite compacts after sintering consisted of an Fe3Si-ordered phase dispersed in an oxide matrix. The DC and AC tests of magnetic composite compacts showed that upon increasing the sintering temperature, the density, magnetic induction, and magnetic permeability increased. The initial magnetic permeability was constant in the entire range of testing frequencies and the magnetic losses increased linearly. The stability of the magnetic characteristics in frequency is promising for developing further such types of magnetic composite. [ABSTRACT FROM AUTHOR]

In 2012, Chen Ning Yang received a 90th birthday gift in the form of a black cube inscribed with his 13 most important contributions, which cover four major areas of physics: statistical mechanics, condensed matter physics, particle physics and field theory. We briefly describe these 13 contributions and make general comments about Yang's distinctive style as a trailblazing leader in research. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the gravitational waves in the context of gauge theory gravity with a negative cosmological constant. The gauge theory gravity is a gravity theory under gauge formulation in the language of geometric algebra. In contrast to general relativity, the background spacetime in gauge theory gravity is flat, the gauge freedom comes from the fact that equations in terms of physical quantities should be kept in a covariant form under spacetime displacement and rotation. Similar to the electromagnetism, the gauge formulation enables us to interpret the gravitational force as a gauge force on the background flat spacetime. The dynamical fields that describe the gravitational interactions are those position and rotation gauge fields introduced as the requirement of the gauge covariance. The gravitational field equations can be derived from the least action principle with the action as a gauge invariant quantity built from the covariant field strength. We discuss the gravitational wave solutions of the field equations with a negative cosmological constant, and show that these solutions are of Petrov type-N. We also discuss the velocity memory effect by calculating the velocity change of an initially free falling massive particle due to the presence of the gravitational waves. [ABSTRACT FROM AUTHOR]

We continue our study of large charge limits of the defect CFT defined by the half-BPS Wilson loop in planar N = 4 supersymmetric Yang-Mills theory. In this paper, we compute 1/J corrections to the correlation function of two heavy insertions of charge J and two light insertions, in the double scaling limit where the charge J and the 't Hooft coupling λ are sent to infinity with the ratio J/ λ fixed. Holographically, they correspond to quantum fluctuations around a classical string solution with large angular momentum, and can be computed by evaluating Green's functions on the worldsheet. We derive a representation of the Green's functions in terms of a sum over residues in the complexified Fourier space, and show that it gives rise to the conformal block expansion in the heavy-light channel. This allows us to extract the scaling dimensions and structure constants for an infinite tower of non-protected dCFT operators. We also find a close connection between our results and the semi-classical integrability of the string sigma model. The series of poles of the Green's functions in Fourier space corresponds to points on the spectral curve where the so-called quasi-momentum satisfies a quantization condition, and both the scaling dimensions and the structure constants in the heavy-light channel take simple forms when written in terms of the spectral curve. These observations suggest extensions of the results by Gromov, Schafer-Nameki and Vieira on the semiclassical energy of closed strings, and in particular hint at the possibility of determining the structure constants directly from the spectral curve. [ABSTRACT FROM AUTHOR]