Yang-Mills Research Articles

Energy loss of a fast moving parton in Gribov-Zwanziger plasma

The Gribov-Zwanziger prescription applied within Yang-Mills theory is demonstrated to be an efficient method for refining the theory’s infrared dynamics. We study the collisional energy loss experienced by a high-energetic test parton as it traverses through the Grivov plasma at finite temperature. To achieve this, we employ a semiclassical approach that considers the parton’s energy loss while accounting for the backreaction induced by the polarization effects due to its motion in the medium. The polarization tensor of the medium is estimated within a nonperturbative resummation considering the Gribov-Zwanziger approach. The modification of the gluon and ghost loops due to the presence of the Gribov parameter plays a vital role in our estimation. We observe that the nonperturbative interactions have a sizable effect on the parton energy loss. Further, we discuss the implications of our findings in the context of relativistic heavy-ion collisions. Published by the American Physical Society 2024

The topological susceptibility slope χ′ of the pure-gauge SU(3) Yang-Mills theory

We determine the pure-gauge SU(3) topological susceptibility slope χ′, related to the next-to-leading-order term of the momentum expansion of the topological charge density 2-point correlator, from numerical lattice Monte Carlo simulations. Our strategy consists in performing a double-limit extrapolation: first we take the continuum limit at fixed smoothing radius, then we take the zero-smoothing-radius limit. Our final result is χ′ = [17.1(2.1) MeV]2. We also discuss a theoretical argument to predict its value in the large-N limit, which turns out to be remarkably close to the obtained N = 3 lattice result.

Retraction: Yang–Mills theory for bundle gerbes (2006 J. Phys. A: Math. Gen. 39 6039)

Retraction: Yang–Mills theory for bundle gerbes (2006 J. Phys. A: Math. Gen. 39 6039)

FeynGrav and Recent Progress in Computational Perturbative Quantum Gravity

This article reviews recent progress in computational quantum gravity caused by the framework that efficiently computes Feynman’s rules. The framework is implemented in the FeynGrav package, which extends the functionality of the widely used FeynCalc package. FeynGrav provides all the tools to study quantum gravitational effects within the standard model. We review the framework, provide the theoretical background for the efficient computation of Feynman rules, and present the proof of its completeness. We review the derivation of Feynman rules for general relativity, Horndeski gravity, Dirac fermions, Proca field, electromagnetic field, and SU(N) Yang–Mills model. We conclude with a discussion of the current state of the FeynGrav package and discuss its further development.

Large N and large representations of Schur line defect correlators

We study the large N and large representation limits of the Schur line defect correlators of the Wilson line operators transforming in the (anti)symmetric, hook and rectangular representations for \U0001d4a9 = 4 U(N) super Yang-Mills theory. By means of the factorization property, the large N correlators of the Wilson line operators in arbitrary representations can be exactly calculated in principle. In the large representation limit they turn out to be expressible in terms of certain infinite series such as Ramanujan’s general theta functions and the q-analogues of multiple zeta values (q-MZVs). Several generating functions for combinatorial objects, including partitions with non-negative cranks and conjugacy classes of general linear groups over finite fields, emerge from the large N correlators. Also we find conjectured properties of the automorphy and the hook-length expansion satisfied by the large N correlators.

Gauge theories and quantum gravity in a finite interval of time on a compact space manifold

We study gauge theories and quantum gravity diagrammatically in a finite interval of time τ, on a compact space manifold Ω. The initial, final, and boundary conditions are formulated in gauge invariant and general covariant ways by means of purely virtual extensions of the theories, which allow us to “trivialize” the local symmetries and switch to invariant fields (the invariant metric tensor, invariant quark, and gluon fields, etc.). The evolution operator U(tf,ti) is worked out for arbitrary initial and final states, as well as general boundary conditions on ∂Ω. We show that U(tf,ti) is well defined and diagrammatically unitary for every τ=tf−ti<∞. The formulation is extended to include purely virtual particles. In quantum gravity, where the cosmological constant ΛC challenges the definition of an S matrix, the results allow us to prove unitarity at τ<∞. We work out the frequencies and eigenfunctions in some explicit examples, including Yang-Mills theory on the finite cylinder. Published by the American Physical Society 2024

BRST symmetry of non-Lorentzian Yang-Mills theory

We explore the realization of BRST symmetry in the non-Lorentzian Yang-Mills Lagrangian within the context of Galilean and Carrollian Yang-Mills theory. Firstly, we demonstrate the nilpotent property of classical BRST transformations and construct corresponding conserve charges for both cases. Then, we analyze the algebra of these charges and observe the nilpotent properties at the algebraic level. The findings of this study contribute to an understanding of BRST symmetry in non-Lorentzian Yang-Mills Lagrangians and provide insights into the algebraic properties of related conserve charges.

A State Space for 3D Euclidean Yang–Mills Theories

It is believed that Euclidean Yang–Mills theories behave like the massless Gaussian free field (GFF) at short distances. This makes it impossible to define the main observables for these theories—the Wilson loop observables—in dimensions greater than two, because line integrals of the GFF do not exist in such dimensions. Taking forward a proposal of Charalambous and Gross, this article shows that it is possible to define Euclidean Yang–Mills theories on the 3D unit torus as ‘random distributional gauge orbits’, provided that they indeed behave like the GFF in a certain sense. One of the main technical tools is the existence of the Yang–Mills heat flow on the 3D torus starting from GFF-like initial data, which is established in a companion paper. A key consequence of this construction is that under the GFF assumption, one can define a notion of ‘regularized Wilson loop observables’ for Euclidean Yang–Mills theories on the 3D unit torus.

Compositional quantum field theory: An axiomatic presentation

We introduce Compositional Quantum Field Theory (CQFT) as an axiomatic model of quantum field theory, based on the principles of locality and compositionality. Our model is a refinement of the axioms of general boundary quantum field theory, and is phrased in terms of correspondences between certain commuting diagrams of gluing identifications between manifolds and corresponding commuting diagrams of state-spaces and linear maps, thus making it amenable to formalization in terms of involutive symmetric monoidal functors and operad algebras. The underlying novel framework for gluing leads to equivariance of CQFT. We study CQFTs in dimension 2 and the algebraic structure they define on open and closed strings. We also consider, as a particular case, the compositional structure of 2-dimensional pure quantum Yang–Mills theory.

On the Global Dynamics of Yang–Mills–Higgs Equations

On the Global Dynamics of Yang–Mills–Higgs Equations

A Nakai–Moishezon Type criterion for supercritical deformed Hermitian–Yang–Mills equation

A Nakai–Moishezon Type criterion for supercritical deformed Hermitian–Yang–Mills equation

Yang–Mills bar connection and holomorphic structure

In this note, we study the Yang–Mills bar connection <inline-formula><tex-math id="M1">\begin{document}$ A $\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2023-0136_M1.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2023-0136_M1.png"/></alternatives></inline-formula>, i.e., the curvature of <inline-formula><tex-math id="M2">\begin{document}$ A $\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2023-0136_M2.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2023-0136_M2.png"/></alternatives></inline-formula> obeys <inline-formula><tex-math id="M3">\begin{document}$ \bar{\partial}_{A}^{\ast}F_{A}^{0,2} = 0 $\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2023-0136_M3.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2023-0136_M3.png"/></alternatives></inline-formula>, on a principal <inline-formula><tex-math id="M4">\begin{document}$ G $\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2023-0136_M4.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2023-0136_M4.png"/></alternatives></inline-formula>-bundle <inline-formula><tex-math id="M5">\begin{document}$ P $\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2023-0136_M5.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2023-0136_M5.png"/></alternatives></inline-formula> over a compact complex manifold <inline-formula><tex-math id="M6">\begin{document}$ X $\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2023-0136_M6.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2023-0136_M6.png"/></alternatives></inline-formula>. According to the Koszul–Malgrange criterion, any holomorphic structure on <inline-formula><tex-math id="M7">\begin{document}$ P $\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2023-0136_M7.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2023-0136_M7.png"/></alternatives></inline-formula> can be seen as a solution to this equation. Suppose that <inline-formula><tex-math id="M8">\begin{document}$ G = SU(2) $\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2023-0136_M8.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2023-0136_M8.png"/></alternatives></inline-formula> or <inline-formula><tex-math id="M9">\begin{document}$ SO(3) $\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2023-0136_M9.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2023-0136_M9.png"/></alternatives></inline-formula> and <inline-formula><tex-math id="M10">\begin{document}$ X $\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2023-0136_M10.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2023-0136_M10.png"/></alternatives></inline-formula> is a complex surface with <inline-formula><tex-math id="M11">\begin{document}$ H^{1}(X,\mathbb{Z}_{2}) = 0 $\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2023-0136_M11.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2023-0136_M11.png"/></alternatives></inline-formula>. We then prove that the <inline-formula><tex-math id="M12">\begin{document}$ (0,2) $\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2023-0136_M12.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2023-0136_M12.png"/></alternatives></inline-formula>-part curvature of an irreducible Yang–Mills bar connection vanishes, i.e., <inline-formula><tex-math id="M13">\begin{document}$ (P,\bar{\partial}_{A}) $\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2023-0136_M13.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2023-0136_M13.png"/></alternatives></inline-formula> is holomorphic.

Two arbitrary-order constraint-preserving schemes for the Yang–Mills equations on polyhedral meshes

<abstract><p>Two numerical schemes are proposed and investigated for the Yang–Mills equations, which can be seen as a nonlinear generalisation of the Maxwell equations set on Lie algebra-valued functions, with similarities to certain formulations of General Relativity. Both schemes are built on the Discrete de Rham (DDR) method, and inherit from its main features: an arbitrary order of accuracy, and applicability to generic polyhedral meshes. They make use of the complex property of the DDR, together with a Lagrange-multiplier approach, to preserve, at the discrete level, a nonlinear constraint associated with the Yang–Mills equations. We also show that the schemes satisfy a discrete energy dissipation (the dissipation coming solely from the implicit time stepping). Issues around the practical implementations of the schemes are discussed; in particular, the assembly of the local contributions in a way that minimises the price we pay in dealing with nonlinear terms, in conjunction with the tensorisation coming from the Lie algebra. Numerical tests are provided using a manufactured solution, and show that both schemes display a convergence in $ L^2 $-norm of the potential and electrical fields in $ \mathcal O(h^{k+1}) $ (provided that the time step is of that order), where $ k $ is the polynomial degree chosen for the DDR complex. We also numerically demonstrate the preservation of the constraint.</p></abstract>

From Maxwell’s equations to Yang-Mills Theory (In celebration to the 70th anniversary of the paper by Yang & Mills)

Celebrando os 70 anos da publicação do artigo de C. N. Yang e R. Mills, este artigo apresenta a construção das chamadas equações de Yang-Mills a partir de requisitos fundamentais, averiguando como se pode formular uma teoria que descreva a auto-interação de bósons vetoriais eletromagneticamente neutros com massa nula. Como estes são atributos do fóton, o ponto de partida são as equações de Maxwell e sua chamada invariância de calibre local, com grupo de simetria U(1). Assim, partindo de um conjunto de campos vetoriais que têm associada uma simetria não-Abeliana global, utilizaremos o chamado método das correntes de Noether para introduzir as auto-interações. O aspecto interessante é que este processo se conclui com a simetria de partida, inicialmente global, tornando-se automaticamente uma simetria de calibre em consequência da estrutura das auto-interações. A abordagem já deixa o caminho construído para a introdução do setor de matéria acoplado minimamente aos campos de Yang-Mills. É importante destacar que este procedimento vai no caminho oposto ao que é apresentado no paper original de Yang-Mills. O procedimento via correntes de Noether é mais natural, visto que responde à questão como partículas elementares de spin-1 podem auto-interagir, sem precisar introduzir o setor de matéria.

The effect of three matters on KSS bound

In this paper, we introduce the black brane solutions in anti-de Sitter (AdS) space in four-dimensional (4D) Einstein–Gauss–Bonnet–Yang–Mills theory in the presence of string cloud and quintessence. Shear viscosity to entropy density ratio is computed via fluid–gravity duality, as a transport coefficient for this model.

Radiation from a gluon-gluino colour-singlet dipole at N3LO

We compute the quantum chromodynamics (QCD) corrections to the decay of a neutralino to gluinos and partons at next-to-next-to-next-to-leading order (N3LO) in the strong coupling constant αs, integrated separately over the phase-space of two, three, four or five particles in the final state. The resulting matrix elements are related to the quark-gluon antenna functions, completing the set of integrated antenna functions in final-final kinematics required for the extension of the antenna subtraction scheme to N3LO. For a model with massless partons (quarks and gluons) and an arbitrary number of adjoint fermions, we obtained the following new results to Oαs3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O}\\left({\\alpha}_s^3\\right) $$\\end{document}: the inclusive cross section for the decay of a neutralino, the renormalization of the effective coupling of a neutralino to a gluino and gluon(s), the gluino collinear anomalous dimension, the gluino contribution to the parton collinear anomalous dimensions and the neutralino-gluino-gluon(s) vertex form factors. A special case of this model is the N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 1 super Yang-Mills theory, where we can relate some of our findings to known results.

A geometric approach to the Yang-Mills mass gap

I provide a new idea based on geometric analysis to obtain a positive mass gap in pure non-abelian renormalizable Yang-Mills theory. The orbit space, that is the space of connections of Yang-Mills theory modulo gauge transformations, is equipped with a Riemannian metric that naturally arises from the kinetic part of reduced classical action and admits a positive definite sectional curvature. The corresponding regularized Bakry-Émery Ricci curvature (if positive) is shown to produce a mass gap for 2+1 and 3+1 dimensional Yang-Mills theory assuming the existence of a quantized Yang-Mills theory on (ℝ1+2, η) and (ℝ1+3, η), respectively. My result on the gap calculation, described at least as a heuristic one, applies to non-abelian Yang-Mills theory with any compact semi-simple Lie group in the aforementioned dimensions. In 2+1 dimensions, the square of the Yang-Mils coupling constant gYM2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {g}_{YM}^2 $$\\end{document} has the dimension of mass, and therefore the spectral gap of the Hamiltonian is essentially proportional to gYM2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {g}_{YM}^2 $$\\end{document} with proportionality constant being purely numerical as expected. Due to the dimensional restriction on 3+1 dimensional Yang-Mills theory, it seems one ought to introduce a length scale to obtain an energy scale. It turns out that a certain ‘trace’ operation on the infinite-dimensional geometry naturally introduces a length scale that has to be fixed by measuring the energy of the lowest glu-ball state. However, this remains to be understood in a rigorous way.

Predicting angular-momentum waves based on Yang–Mills equations

As one of the most elegant theories in physics, Yang–Mills (YM) theory not only incorporates Maxwell’s equations unifying electromagnetism, but also underpins the standard model explaining the electroweak and strong interactions in a succinct way. Whereas the highly nonlinear terms in YM equations involving the interactions between potentials and fields retard the resolution for them. In the U(1) case, the solutions of Maxwell’s equations are the electromagnetic waves, which have been applied extensively in the modern communication networks all over the world. Likewise the operator solutions of the YM equations under the assumptions of weak-coupling and zero-coupling predict the SU(2) angular-momentum waves, which is the staple of this work. Such angular-momentum waves are hopefully realized in the experiments through the oscillation of spin angular momentum, such as the “spin Zitterbewegung” of Dirac’s electron.

Energy estimates of Yang–Mills functional

In this paper, we use the Uhlenbeck compactness theorem and Lojasiewicz–Simon gradient inequality of the Yang–Mills [Formula: see text]-energy functional to prove some energy properties of Yang–Mills connections. In particular, we can get the discreteness of Yang–Mills energy from the compactness of the moduli space of Yang–Mills connections.

Celestial holography and AdS3/CFT2 from a scaling reduction of twistor space

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 ℙ\U0001d54a 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 ℙ\U0001d54a, 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.