Arbitrary Gauge Research Articles

Toward double copy on arbitrary backgrounds

Abstract Double copy relates scattering amplitudes in a web of gravitational and gauge theories. Although it has seen great success when applied to amplitudes in vacuum, far less is known about double copy in arbitrary gravitational and gauge backgrounds. Focussing on the simplest pair production amplitudes of scalar QCD in a background gauge field, we construct, at next-to-leading order in perturbation theory, a double copy map to particle production in general metrics (and associated axio-dilatons) constructed from the gauge background. We connect our results to convolutional and classical double copy and, turning to examples, identify a class of gauge fields which generate FRW spacetimes via double copy. For this case we are able to conjecture the all-orders form of the double copy map.

Gauged Gaussian projected entangled pair states: A high dimensional tensor network formulation for lattice gauge theories

Gauge theories form the basis of our understanding of modern physics—ranging from the description of quarks and gluons to effective models in condensed matter physics. In the nonperturbative regime, gauge theories are conventionally treated discretely as lattice gauge theories. The resulting systems are evaluated with path-integral based Monte Carlo methods. These methods, however, can suffer from the sign problem and do not allow for a direct evaluation of real-time dynamics. In this work, we present a unified and comprehensive framework for gauged Gaussian projected entangled pair states (PEPS), a variational ansatz based on tensor networks. We review the construction of Hamiltonian lattice gauge theories, explain their similarities to PEPS, and detail the construction of the ansatz state. The estimation of ground states is based on a variational Monte Carlo procedure with the PEPS as an ansatz state. This sign-problem-free ansatz can be efficiently evaluated in any dimension with arbitrary gauge groups, and can include dynamical fermionic matter, suggesting new options for the simulation of nonperturbative regimes of gauge theories, including quantum chromodynamics. Published by the American Physical Society 2024

Automatic generation of helicity amplitudes in the Feynman-diagram gauge

We develop a method to calculate helicity amplitudes of an arbitrary tree-level process in the Feynman-diagram (FD) gauge for an arbitrary gauge model with adraph5_a@. We start from the ’t Hooft–Feynman gauge Lagrangian in eynules and generate scattering amplitudes by identifying the Goldstone boson as the 5th component of each weak boson. All the vertices of the 5-component weak bosons are then created automatically by assembling the relevant weak boson and Goldstone boson vertices in the Feynman gauge. The 5-component weak boson vertices are then connected by the 5×5 matrix propagator in the FD gauge. As a demonstration of the method we calculate the cross section for the process μ−μ+→νμν¯μtt¯H with complex top Yukawa coupling, which can be obtained by adding a gauge invariant dimension-6 operator to the Standard Model (SM) Lagrangian. The FD gauge and the unitary (U) gauge amplitudes give exactly the same cross section, and subtle gauge theory cancellation among diagrams in the U gauge at high energies is absent in the FD gauge, as has been observed for various SM processes. In addition, we find that the total cross sections at high energies are dominated by a single, or a set of nonvanishing Feynman amplitudes with the higher dimensional vertices in the FD gauge. Published by the American Physical Society 2024

What can abelian gauge theories teach us about kinematic algebras?

The phenomenon of BCJ duality implies that gauge theories possess an abstract kinematic algebra, mirroring the non-abelian Lie algebra underlying the colour information. Although the nature of the kinematic algebra is known in certain cases, a full understanding is missing for arbitrary non-abelian gauge theories, such that one typically works outwards from well-known examples. In this paper, we pursue an orthogonal approach, and argue that simpler abelian gauge theories can be used as a testing ground for clarifying our understanding of kinematic algebras. We first describe how classes of abelian gauge fields are associated with well-defined subalgebras of the diffeomorphism algebra. By considering certain special subalgebras, we show that one may construct interacting theories, whose kinematic algebras are inherited from those already appearing in a related abelian theory. Known properties of (anti-)self-dual Yang-Mills theory arise in this way, but so do new generalisations, including self-dual electromagnetism coupled to scalar matter. Furthermore, a recently obtained non-abelian generalisation of the Navier-Stokes equation fits into a similar scheme, as does Chern-Simons theory. Our results provide useful input to further conceptual studies of kinematic algebras.

Unitarity constraints on large multiplets of arbitrary gauge groups

We impose partial-wave unitarity on 2→2 tree-level scattering processes to derive constraints on the dimensions of large scalar and fermionic multiplets of arbitrary gauge groups. We apply our results to scalar and fermionic extensions of the Standard Model, and also to the Grand Unified Theories (GUTs) based on the groups SU(5), SO(10), and E6. We find scenarios within the latter two GUTs that violate the unitarity condition; this may require a reevaluation of the validity of perturbation theory in those scenarios.

Topological twists of massive SQCD, Part I

We consider topological twists of four-dimensional N=2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {N}=2$$\\end{document} supersymmetric QCD with gauge group SU(2) and Nf≤3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N_f\\le 3$$\\end{document} fundamental hypermultiplets. The twists are labelled by a choice of background fluxes for the flavour group, which provides an infinite family of topological partition functions. In this Part I, we demonstrate that in the presence of such fluxes the theories can be formulated for arbitrary gauge bundles on a compact four-manifold. Moreover, we consider arbitrary masses for the hypermultiplets, which introduce new intricacies for the evaluation of the low-energy path integral on the Coulomb branch. We develop techniques for the evaluation of these path integrals. In the forthcoming Part II, we will deal with the explicit evaluation.

Entanglement and confinement in lattice gauge theory tensor networks

We develop a transfer operator approach for the calculation of Rényi entanglement entropies in arbitrary (i.e. Abelian and non-Abelian) pure lattice gauge theory projected entangled pair states in 2+1 dimensions. It is explicitly shown how the long-range behavior of these quantities gives rise to an entanglement area law in both the thermodynamic limit and in the continuum. We numerically demonstrate the applicability of our method to the ℤ2 lattice gauge theory and relate some entanglement properties to the confinement-deconfinement transition therein. We provide evidence that Rényi entanglement entropies in certain cases do not provide a complete probe of (de)confinement properties compared to Wilson loop expectation values as other genuine (nonlocal) observables.

Explicit no- π2 renormalization schemes in QCD at five loops

We examine a variety of renormalization schemes in QCD based on its 3-point vertices where the β-functions, gluon, ghost, quark and quark mass anomalous dimensions in each scheme do not depend on ζ4 or ζ6 in an arbitrary linear covariant gauge at five loops. We comment on the C-scheme. Published by the American Physical Society 2024

Synchronous coordinates and gauge-invariant observables in cosmological spacetimes

We consider the relational approach to construct gauge-invariant observables in cosmological perturbation theory using synchronous coordinates. We construct dynamical synchronous coordinates as non-local scalar functionals of the metric perturbation in the fully non-linear theory in an arbitrary gauge. We show that the observables defined in this dynamical coordinate system are gauge-independent, and that the full perturbed metric has the expected form in these coordinates. Our construction generalises the familiar synchronous gauge in linearised gravity, widely used in cosmological perturbation theory, to the non-linear theory. We also work out the expressions for the gauge-invariant Einstein equation, sourced either by an ideal fluid or a scalar field up to second order in perturbation theory, and give explicit expressions for the Hubble rate—as measured by synchronous observers or by observers co-moving with the matter field—up to that order. Finally, we consider quantised linear perturbations around Minkowski and de Sitter backgrounds, and compute the two-point function of the gauge-invariant metric perturbation in synchronous coordinates, starting with two-point function in a general linear covariant gauge. Although the gauge-fixed two-point function contains gauge modes, we show that the resulting gauge-invariant two-point function only contains the physical tensor modes and it is thus positive, i. e. it has a spectral representation.

Background Independence and the Adler–Bardeen Theorem

We prove that for renormalizable Yang–Mills gauge theory with arbitrary compact gauge group (of at most a single abelian factor) and matter coupling, the absence of gauge anomalies can be established at the one-loop level. This proceeds by relating the gauge anomaly to perturbative agreement, which formalizes background independence.

Critical Properties of Three-Dimensional Many-Flavor QEDs

We review several variants of three-dimensional quantum electrodynamics (QED3) with Nf fermion (or boson) flavors, including fermionic (or spinorial) QED3, bosonic (or scalar) QED3, N=1 supersymmetric QED and also models of reduced QED (supersymmetric or not). We begin with an introduction to these models and their flow to a stable infra-red fixed point in the large-Nf limit. We then present detailed state-of-the-art computations of the critical exponents of these models within the dimensional regularization (and reduction) scheme(s), at the next-to-leading order in the 1/Nf expansion and in an arbitrary covariant gauge. We finally discuss dynamical (matter) mass generation and the current status of our understanding of the phase structure of these models.

FeynGrav 2.0

We present a new version of FeynGrav. The present version supports Feynman rules for matter with non-vanishing mass and SU(N) Yang-Mills model. We revisit the gauge fixing procedure for gravity and derive interaction rules valid for an arbitrary gauge fixing parameter. We provide a few simple examples of calculations to illustrate package usage. Program summaryProgram Title: FeynGravCPC Library link to program files:https://doi.org/10.17632/rwnrbbdkkv.1Developer's repository link:github.com/BorisNLatosh/FeynGravLicensing provisions: GPLv3Programming language: Wolfram Mathematica 10 and higherExternal routines/libraries: FeynCalc [1,2]Nature of problem: FeynGrav is a software package that simplifies calculations involving the Feynman rules for gravity. These rules are complex and consist of numerous terms, but FeynGrav makes it possible to work with a specific set of rules within the FeynCalc environment. The package includes interaction rules for regular matter with different spin values, as well as for the SU(N) Yang-Mills model in curved spacetime and general relativity. FeynGrav provides scripts to generate the relevant interaction rules and libraries of pre-generated expressions, making it a powerful tool for researchers in the field of theoretical physics.Solution method: I propose a framework that provides a straightforward way to obtain expressions for the corresponding Feynman rules by efficiently utilizing perturbative expansions. In particular, within the perturbative approach to quantum gravity, certain quantities admit finite perturbative expansions, while others have infinite perturbative expansions. I derive formulas that allow the generation of terms with infinite expansions for any given order of perturbation theory. In all actions describing gravitational interactions, all derivatives can be placed on terms with finite perturbative expansions via integration by parts. In this way, the proposed framework gives a simple algorithm for deriving Feynman rules.Additional comments including restrictions and unusual features: Scripts responsible for generating interaction rules are placed in the “Rules” folder. They can be used separately and only require FeynCalc to run. The “Libs” folder contains the “FeynGravLibrariesGenerator.wl” script and the libraries it generates. “FeynGrav.wl” is the main package file that imports data from the libraries and uses it to work with the interaction rules. The file “FeynGrav_Examples.nb” contains examples of calculations.

Extending the reach of the point-to-set principle

The point-to-set principle of J. Lutz and N. Lutz (2018) has recently enabled the theory of computing to be used to answer open questions about fractal geometry in Euclidean spaces Rn. These are classical questions, meaning that their statements do not involve computation or related aspects of logic.In this paper we extend the reach of the point-to-set principle from Euclidean spaces to arbitrary separable metric spaces X. We first extend two algorithmic dimensions—computability-theoretic versions of classical Hausdorff and packing dimensions that assign dimensions dim⁡(x) and Dim(x) to individual pointsx∈X—to arbitrary separable metric spaces and to arbitrary gauge families. Our first two main results then extend the point-to-set principle to arbitrary separable metric spaces and to a large class of gauge families.We demonstrate the power of our extended point-to-set principle by using it to prove new theorems about classical fractal dimensions in hyperspaces.

Perturbative aspects of CPT -even Lorentz-violating scalar chromodynamics

In this work, we formulate the theory of Lorentz-violating scalar Quantum Chromodynamics with an arbitrary non-Abelian gauge group. This theory belongs to the class of models encompassed by the standard model extension framework. At the lowest order in the theory's Lorentz violation parameters, we calculate the divergent quantum corrections, including the renormalization group $\beta$-functions of the theory. The Lorentz-violating sector is shown to be scale invariant if there is a particular relation between the couplings.

One-loop fermion-photon vertex in arbitrary gauge and dimensions: A novel approach

We compute a one-loop electron-photon vertex with fully off-shell external momenta in an arbitrary covariant gauge and space-time dimension. There exist numerous efforts in literature where a one-loop off-shell vertex is calculated by employing the standard first-order Feynman rules in different covariant gauges and space-time dimensions of interest. The tensor structure which decomposes this three-point vertex into the components transverse and longitudinal to the photon momentum gets intertwined in this first-order formalism. The Ward-Takahashi identity is explicitly invoked to untangle the two pieces and the results are expressed in a preferred basis of 12 spin amplitudes. We propose a novel approach based upon an efficient combination of the first- and second-order formalisms of quantum electrodynamics to compute this one-loop vertex. Among some conspicuous advantages is the fact that this less known second-order formalism separates the spin and scalar degrees of freedom of an electron interacting electromagnetically. More noticeably, the longitudinal and transverse contributions naturally disentangle from the onset in our approach. Moreover, this decomposition leads to identities between one-loop scalar Feynman integrals with higher powers in the propagators and shifted space-time dimensions that can be used to prove the Ward-Takahashi identity at one-loop order without the need to evaluate any Feynman integral. Additionally, this natural decomposition allows us to establish the gauge independence of the Pauli form factor through explicit cancellations of scalar Feynman integrals that depend on the gauge parameter. These cancellations naturally lead to a compact expression for the Pauli form factor in arbitrary dimensions. Wherever necessary and insightful, we make comparisons with earlier works.

Gauge invariance and finite counterterms in chiral gauge theories

We derive the finite one-loop counterterm required to restore the Ward Identities broken by the regularization scheme in chiral gauge theories. Our result is an analytic expression applicable to a wide class of regularizations satisfying a few general properties. We adopt the background field method, which ensures background gauge invariance in the quantized theory, and focus on renormalizable chiral theories with arbitrary gauge group and fermions in general representations. Our approach can be extended to theories involving scalars, such as the Standard Model, or to non-renormalizable theories, such as the SMEFT. As a concrete application, we work out the finite counterterm at one loop in the Standard Model, within dimensional regularization and the Breitenlohner-Maison-’t Hooft-Veltman prescription for γ5.

D4-branes wrapped on four-dimensional orbifolds through consistent truncation

We construct a consistent truncation of six-dimensional matter coupled F(4) gauged supergravity on a cornucopia of two-dimensional surfaces including a spindle, disc, domain wall and other novel backgrounds to four-dimensional minimal gauged supergravity. Using our consistent truncation we uplift known AdS2× Σ1 solutions giving rise to four-dimensional orbifold solutions, AdS2× Σ1 ⋉ Σ2. We further uplift our solutions to massive type IIA supergravity by constructing the full uplift formulae for six-dimensional U(1)2-gauged supergravity including all fields and arbitrary Romans mass and gauge coupling. The solutions we construct are naturally interpreted as the near-horizon geometries of asymptotically AdS6 black holes with a four-dimensional orbifold horizon. Alternatively, one may view them as the holographic duals of superconformal quantum mechanical theories constructed by compactifying five-dimensional USp(2N) theory living on a stack of D4-D8 branes on the four-dimensional orbifolds. As a first step to identifying these quantum mechanical theories we compute the Bekenstein-Hawking entropy holographically.

Electron mass anomalous dimension at [formula omitted] in three-dimensional [formula omitted] supersymmetric QED

We consider massless three-dimensional N=1 supersymmetric quantum electrodynamics (QED) with Nf flavours of electrons. Within the dimensional reduction scheme, we compute the critical exponents corresponding to both the electron and selectron field and (parity-even) mass anomalous dimensions at the next-to-leading order in the 1/Nf expansion and in an arbitrary covariant gauge. The equality of the gauge-invariant mass anomalous dimensions of the electron and the selectron is found to result from a subtle role played by the epsilon-scalars. Our general framework also allows us to compute the critical exponents of pure scalar QED and to recover known results in the case of spinor QED. An application of our results to dynamical (s)electron mass generation is considered. We find evidence that, while dynamical flavor symmetry breaking occurs in spinor QED, both pure scalar QED and supersymmetric QED remain in an interacting conformal phase.

Toda equations for surface defects in SYM and instanton counting for classical Lie groups

The partition function of super Yang-Mills theories with arbitrary simple gauge group coupled to a self-dual Ω background is shown to be fully determined by studying the renormalization group equations relevant to the surface operators generating its one-form symmetries. The corresponding system of equations results in a non-autonomous Toda chain on the root system of the Langlands dual, the evolution parameter being the RG scale. A systematic algorithm computing the full multi-instanton corrections is derived in terms of recursion relations whose gauge theoretical solution is obtained just by fixing the perturbative part of the IR prepotential as its asymptotic boundary condition for the RGE. We analyze the explicit solutions of the τ-system for all the classical groups at the diverse levels, extend our analysis to affine twisted Lie algebras and provide conjectural bilinear relations for the τ-functions of linear quiver gauge theory.

Tensor current renormalization in the RI′ scheme at four loops

To assist the matching of lattice field theory results to the high energy continuum limit we evaluate the Green's function where the tensor quark bilinear operator is inserted at zero momentum in a quark 2-point function for an arbitrary covariant gauge. This is carried out in both the $\overline{\mathrm{MS}}$ and ${\mathrm{RI}}^{\ensuremath{'}}$ schemes to four loops. The tensor current anomalous dimension is also calculated to four loops in both schemes for an arbitrary color group.