<list id='lst0001'><list-item id='lstitem0001'><label>&#8226;</label><para id='p0001'>Exact plane-wave solutions of SU(2) Yang-Mills equations: complete classification.</para></list-item><list-item id='lstitem0002'><label>&#8226;</label><para id='p0002'>Genuinely non-Abelian waves require <italic>&#946;</italic>&#8239;&#215;&#8239;&#8467;&#8239;&#8800;&#8239;0 and contain a nonlinear second harmonic.</para></list-item><list-item id='lstitem0003'><label>&#8226;</label><para id='p0003'>Zero-action family links vacuum to non-Abelian waves; energy grows nonlinearly.</para></list-item></list>

China

Yu-Xuan Zhang

Jing-Ling Chen

A genuinely non-Abelian plane-wave solution of the SU(2) Yang-Mills equations

We construct static, spherically symmetric, and asymptotically flat colored black holes in four-dimensional Einstein gravity coupled to logarithmic nonlinear Yang–Mills theory with gauge group SU(2). Unlike exact solutions based on the Wu–Yang ansatz, these configurations contain a dynamical radial gauge amplitude and arise from a fully coupled boundary-value problem. An integral identity establishes that nontrivial magnetically neutral solutions must be nodal. We obtain the fundamental one-node branch and verify its smooth convergence to the ordinary Einstein–Yang–Mills colored black hole in the weakly nonlinear regime. Increasing the logarithmic nonlinearity lowers the ADM mass, raises the Hawking temperature, and shifts the gauge-field node outward. No termination of the branch is detected within the parameter and radial ranges investigated; instead, the exterior geometry approaches Schwarzschild on fixed radial domains while the colored field develops an increasingly extended tail. A characteristic analysis shows that sufficiently strong logarithmic deformations lose hyperbolicity near the event horizon, restricting their dynamical interpretation. Although the non-Abelian hair carries no independent asymptotic charge, it leaves a subleading gravitational imprint. For representative solutions within the investigated parameter and radial ranges, the numerical interior evolution detects neither an inner Cauchy horizon nor oscillatory mass inflation. Their mass function approaches a finite limit, while the center remains a Schwarzschild-type spacelike curvature singularity. The recovery of the linear theory is nonuniform near the center, where every finite nonlinear deformation eventually enters the strongly logarithmic regime. Temperature turning points also mark changes of local thermodynamic stability, without implying a global phase transition.

Brazil

Celio Muniz

Colored black holes in logarithmic nonlinear Yang–Mills theory

We continue the study of flux tubes in confining gauge theories placed in a rigid AdS background, focusing on the three-dimensional case. Our analysis is performed in the large-radius regime, where effective string theory provides a good approximation of the dynamics. Using a combination of techniques, primarily the analytic transcendentality ansatz bootstrap, we compute observables up to two-loop order in the expansion in powers of the string length over the AdS radius, which constitutes the main result of this work. Finally, we employ Padé resummations to explore the possible compatibility of our results with a smooth interpolation of observables between large-radius AdS and small-radius AdS, in which gauge theory is weakly coupled.

Switzerland

Barak Gabai

Victor Gorbenko

Bendeguz Offertaler

Yang-Mills flux tube in AdS. Part II. Effective String Theory

Within the wide variety of topological solitons supported by Yang-Mills theory, merons occupy a particularly distinguished role. Despite their simplicity, they represent genuinely non-Abelian configurations that can be regarded as the fundamental building blocks of instantons, and they provide a qualitatively accurate picture of confinement. In this work, we show that such configurations are, in fact, supported by a broad class of non-Abelian gauge theories beyond Yang-Mills, provided that suitable physical conditions are satisfied. Taking into account their gravitational backreaction, we further demonstrate that both black holes and Euclidean wormholes sourced by merons admit natural extensions within this generalized framework, which regularizes the singular behavior they exhibit in constant-curvature backgrounds. As a byproduct, we construct a regular black hole solution supported by genuinely non-Abelian gauge fields, based on a non-Abelian generalization of the Ayón-Beato-García nonlinear electrodynamics. As a consequence, physical effects intrinsic to merons are likewise expected to be inherited by these classes of theories beyond the Yang-Mills framework. A notable example is the spin from isospin effect, whereby bosonic excitations charged under the gauge group can effectively behave as fermionic degrees of freedom.

Mexico

Borja Diez

Chile

Luis Guajardo

Merons beyond Yang-Mills theory

We explore the relation between geometry, topology and entanglement for quantum states in two-dimensional Yang-Mills theory. The most familiar class of states in this theory are states defined by Euclidean path integrals over Riemann surfaces. Bipartite states of this class have thermofield double structure, with entanglement consistently reducing with total area and the number of topological defects, becoming separable in the infinite-area limit. In contrast, Wilson lines and loops generate rich non-monotonic behavior of the entanglement entropy. Most notably, we find that for a certain discrete set of configurations, entanglement remains finite at infinite area. The reduced density matrices, in such configurations, take the form of finite-dimensional projectors onto non-trivial vacuum sectors. We also discuss the implications of the large-volume effects for confinement and find that special asymptotic configurations are related to transitions in the confining force.

Dmitry Melnikov

Jefferson Oliveira

Valmir Peixoto

Marcia Tenser

States of 2D Yang-Mills and large-volume entanglement

Yang-Mills theories at $\textit{θ}$ and $\textit{θ}$+2$\textit{π}$ are unitarily equivalent, but their 2$\textit{π}$ periodicity has a nontrivial realization. Recent developments in generalized symmetries rigorously prove that confinement vacua at $\textit{θ}$ = 0 and 2$\textit{π}$ should belong to different symmetry-protected topological (SPT) states with the 1-form center symmetry. For its examination, we measure the Wilson-’t Hooft loop operators at $\textit{θ}$ = 2$\textit{π}$ for the SU(2) Wilson lattice gauge action and discuss their long-distance behaviors. This requires us to identify the gauge topological charge in the presence of defects, and we employ the 1-form covariant DBW2 gradient flow to smear lattice gauge fields. We find a clear perimeter-law signal for the dyonic Wilson-’t Hooft loop at $\textit{θ}$ = 2$\textit{π}$, providing numerical evidence in the pure SU(2) Yang-Mills theory for the theoretically expected dyon condensation at $\textit{θ}$ = 2$\textit{π}$.

Japan

Hiromasa Watanabe

Issaku Kanamori

Okuto Morikawa

Yuki Nagai

Yuya Tanizaki

Akio Tomiya

Numerical hints for dyon condensation at $\textit{θ}$ = 2$\textit{π}$ via Wilson-’t Hooft loops in SU(2) Yang-Mills theory

Bern-Carrasco-Johansson relations are helicity-independent constraints among the partial amplitudes of tree-level processes containing gluons and possibly also matter fields. They are a consequence of color-kinematic duality, but alternatively can be derived using the color-factor symmetry of tree-level amplitudes. We use recursive perturbiner methods to present a general, streamlined proof of the color-factor symmetry of all tree-level amplitudes containing an arbitrary number of fundamental spin-zero or spin-one-half matter fields and at least one gluon.

United States

Abigail Chriss

Mia Karlsson

Stephen Naculich

Color-factor symmetry using perturbiner methods for tree-level amplitudes of Yang-Mills theory coupled to matter

<p>We study the confinement phase transition (PT) in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>SU</mi><mo stretchy="false">(</mo><msub><mrow><mi>N</mi></mrow><mrow><mi>c</mi></mrow></msub><mo stretchy="false">)</mo></mrow></math> pure Yang-Mills theory at finite <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>θ</mi><mo>≠</mo><mn>0</mn></math> using the improved holographic QCD (IHQCD) model. We show that the maximal amount of supercooling is reduced in the confinement PT as a function of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>θ</mi></math> for large but fixed <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>c</mi></msub></math>. Upon completion of the confinement PT, a network of domain walls can be produced, owing to the multibranched vacuum structure of Yang-Mills theory at finite <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>θ</mi></math>. We highlight the potential interplay between the produced domain walls and the confinement PT dynamics. We emphasize that domain wall production from bubble coalescence in strongly coupled nonconformal first order PTs is a dynamical process of vacuum assignment, hydrodynamics, and local reheating effects, all potentially affecting the approach toward the scaling regime. Lastly, we demonstrate the level of tuning necessary for potentially interesting imprints from gravitational waves through domain wall annihilation and its interplay with the confinement PT.</p>

Italy

Bruno Missoni

Enrico Morgante

Nicklas Ramberg

Domain walls from confining bubbles: SU(N) Yang-Mills theory at finite <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>θ</mi></mrow></math>

In this work, we construct a BRST-exact quartet mechanism in <italic>SU</italic>(3) Yang-Mills theory in the Landau gauge. The quartet sector is cohomologically trivial in the standard vacuum, ensuring equivalence to pure Yang-Mills theory. The transformation rules carry both commutator and anticommutator structures, enlarging the field content from eight to nine degrees of freedom.

M.M. Amaral

V.E.R. Lemes

Background-equivariant BRST observables and i-particle propagators from an auxiliary quartet in SU(3) Yang-Mills

Motivated by applications of self-dual theories to the AdS/CFT correspondence, we study self-dual Yang–Mills theory (SDYM) and its relation to Yang–Mills theory and to Chalmers–Siegel theory with Dirichlet, Neumann, and mixed boundary conditions. A Fefferman–Graham analysis of SDYM is performed to identify its boundary CFT data. We make a proposal for self-dual holography that defines 3$\textit{d}$ “self-dual CFTs”. The bulk-to-bulk and boundary-to-bulk propagators for SDYM and for Yang–Mills/Chalmers–Siegel theory with mixed boundary conditions are derived in Feynman and axial gauges. Three- and four-point functions are computed in the spinor-helicity formalism, and the relations among the results in the various theories are clarified. The flat limit and the gauge-(in)dependence of the results are analyzed.

Belgium

Russia

Evgeny Skvortsov

Richard Dongen

Dirichlet, Neumann, mixed and self-dual holography: (self-dual) Yang–Mills theory