We generalize the analysis of the asymptotic higher spin symmetries developed in the first three parts of this series by considering the minimal coupling of Einstein Gravity and Yang-Mills theory. We show that there exist symmetry parameters that satisfy a collection of dual equations of motion, which allow the construction of an infinite collection of charges that are conserved in the absence of radiation. These Noether charges act on the Einstein Yang-Mills phase space canonically and non-linearly. Their action defines a symmetry algebroid which reduces to a symmetry algebra at non-radiative cuts and generalizes the celestial $\textit{sw}$ algebra. The corresponding symmetry bracket is shown to satisfy the Jacobi identity and an interesting cross-product structure, which is analyzed in details.

Canada

Nicolas Cresto

Laurent Freidel

Asymptotic higher spin symmetries. Part IV. Einstein-Yang-Mills theory

We extend previous computations of Hermitian Yang–Mills connections for bundles on complete intersection Calabi–Yau manifolds to bundles on their free quotients. Bundles on quotient manifolds are often defined by equivariant bundles on corresponding covering spaces. Combining equivariant structure and the generalized Donaldson algorithm, we develop a systematic approach to compute connections of holomorphic poly-stable bundles on quotient manifolds. With it, we construct connections of an SU(3) bundle on a <math altimg='si1.svg'><msub><mi mathvariant='double-struck'>Z</mi><mn>5</mn></msub></math> quotient of the quintic and an SU(5) bundle on a <math altimg='si4.svg'><mrow><msub><mi mathvariant='double-struck'>Z</mi><mn>3</mn></msub><mo linebreak='goodbreak'>&#215;</mo><msub><mi mathvariant='double-struck'>Z</mi><mn>3</mn></msub></mrow></math> quotient of the bi-cubic. For both examples, the algorithm converges as expected and gives a good approximation of Hermitian Yang&#8211;Mills connections, which will be important for heterotic model building in Calabi&#8211;Yau compactifications.

China

Wei Cui

Numerical hermitian yang-Mills connection for bundles on quotient manifold

We present a prescription for computing tree-level scattering amplitudes in 10D super-Yang-Mills (SYM) theory using the pure spinor worldline formalism. The pure spinor formalism has proven to be a powerful framework for studying supersymmetric field theories, providing manifestly covariant and BRST-invariant formulations of amplitudes. By incorporating the worldline approach, we construct a first-quantized representation of SYM amplitudes in 10D, where interactions are encoded through the insertion of vertex operators along the particle’s trajectory. We explicitly compute the N-point function, demonstrating an agreement with the $\textit{α}$ $\textit{→}$ 0 limit of open superstring amplitudes and confirming that the kinematic numerators satisfy the expected BRST relations. Our results establish the pure spinor worldline formalism as a tool for studying scattering amplitudes and suggest further applications to 11D supergravity.

Sweden

Brazil

Max Guillen

United States

Marcelo Santos

United Kingdom

Spain

Eggon Viana

The pure spinor superparticle and 10D super-Yang-Mills amplitudes

We apply the positivity bootstrap approach to SU(3) lattice Yang-Mills (YM) theory, extending previous studies of large N and SU(2) theories by incorporating multiple-trace Wilson loop operators. By utilizing Hermitian and reflection positivity conditions, alongside Schwinger-Dyson (SD) loop equations, we compute rigorous bounds for the expectation values of plaquette Wilson loops in 2D, 3D, and 4D YM theories. Our results exhibit clear convergence and are consistent with known analytic or numerical results. To enhance the approach, we introduce a novel twist-reflection positivity condition, which we prove to be exact in 2D YM theory. Additionally, we propose a dimensional-reduction truncation, where Wilson loop operators are effectively restricted to a lower-dimensional subplane, significantly simplifying computations. SD equations for double-trace Wilson loops are also derived in detail. Our findings suggest that the positivity bootstrap method is broadly applicable to higher-rank gauge theories beyond single-trace cases, providing a solid foundation for further non-perturbative investigations of gauge theories using positivity-based methods.

Yuanhong Guo

Zeyu Li

Gang Yang

Guorui Zhu

Bootstrapping SU(3) lattice Yang-Mills theory

<p>We propose a bosonic string dual to large <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>N</mi></mrow></math> chiral Yang-Mills theory in two dimensions at finite `t Hooft coupling. The worldsheet theory is a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>β</mi><mtext>−</mtext><mi>γ</mi></mrow></math> system deformed by a chiral Polchinski-Strominger term. We reproduce the partition function on a torus, cylinder three-point amplitudes, and the area law for Wilson loops. We also present candidate string duals to symmetric product orbifolds for general seed conformal field theories with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>c</mi><mo>&lt;</mo><mn>24</mn></math> and their <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>T</mi><mover accent="true"><mrow><mi>T</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>J</mi><mover accent="true"><mrow><mi>T</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow></math> deformations. The results hint at interrelations among confining, nonrelativistic, and matrix strings and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>AdS</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>/</mo><mrow><msub><mrow><mi>CFT</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></mrow></math>.</p>

CERN

Shota Komatsu

Switzerland

Pronobesh Maity

String Duals of Two-Dimensional Yang-Mills Theory and Symmetric Product Orbifolds

In this paper, wave solutions to the classical Yang-Mills equations with <italic>SU</italic>(2) symmetry are investigated in the region outside field sources. They represent a significant generalization of the solutions found in our previous publication describing non-Abelian transverse progressive waves propagating in the direction of the Cartesian <italic>z</italic>-axis. In the new paper, wave solutions to the considered system of nonlinear partial differential equations are sought in a special form. In it, the unknown functions are presented as some complex series and for their coefficients, depending on the wave phase, a system of recurrence relations is obtained. This paper proves that in the examined region, the considered complex series are absolutely convergent. They allow us to determine a wide class of non-Abelian wave solutions to the Yang-Mills equations. In addition, exact wave solutions in closed form are found, which describe the asymptotic behavior of the considered non-Abelian wave solutions for large distances from the <italic>z</italic>-axis.

Russia

Alexander S. Rabinowitch

On a wide class of solutions of SU(2) Yang–Mills equations describing non-Abelian progressive waves

We study the thermodynamics of Einstein–Power–Yang–Mills AdS black holes via the Euclidean path integral method, incorporating appropriate boundary and counterterms. By analyzing unstable timelike and null circular geodesics, we demonstrate that their Lyapunov exponents reflect the thermodynamic phase structure obtained from the Euclidean action. Specifically, the small-large black hole phase transition, analogous to a van der Waals fluid, is signaled by a discontinuity in the Lyapunov exponent. Treating this discontinuity as an order parameter, we observe a universal critical exponent of 1/2, consistent with mean-field theory. These results extend previous insights from black hole spacetimes with Abelian charges to scenarios involving nonlinear, non-Abelian gauge fields, highlighting the interplay between black hole thermodynamics and chaotic dynamics.

India

R. Karthik

D. Dillirajan

K. Ajith

Kartheek Hegde

Shreyas Punacha

Croatia

A. Kumara

Euclidean thermodynamics and Lyapunov exponents of Einstein–Power–Yang–Mills AdS black holes

We obtain inequivalent classical r-matrices of the <italic>osp</italic>(1|2) Lie superalgebra as real solutions of the graded (modified) classical Yang-Baxter equation, in such a way that the corresponding automorphism transformation is employed. Then, Yang-Baxter deformations of the Wess-Zumino-Witten model based on the OSP(1|2) Lie supergroup are specified by super skew-symmetric classical r-matrices. In this regard, the effect coming from the deformation is reflected as the coefficient of both metric and <italic>B</italic>-field. Furthermore, it is shown that all resulting classical r-matrices are non-Abelian and also non-unimodular, which leads us to graded generalized supergravity equations. We show that the background of undeformed model is a solution of the graded generalized supergravity equations when supplemented by an appropriate supervector field obtaining from the linear combination of the Killing supervectors corresponding to the background, while the deformed models do not satisfy these equations. This is consistent with our expectations, since the deformed models under consideration do not describe a Green-Schwarz superstring. However, the deformed backgrounds are interesting, in particular in the OSP(1|2) case they are rare, much hard technical work was needed to obtain them.

Iran

Ali Eghbali

Yaghoub Samadi

Adel Rezaei-Aghdam

Yang-Baxter deformations of the OSP(1|2) WZW model

Astrophysical black holes (BHs) are inevitably surrounded by dark matter halos and plasma environments, yet most theoretical studies idealize them as isolated vacuum solutions. Bridging this gap requires understanding how non-Abelian gauge fields and dark matter jointly modify BH geometry, thermodynamics, and observational signatures—a challenge compounded by quantum gravitational effects that become crucial during late-stage evaporation. We investigate Yang-Mills (YM) charged BHs embedded in perfect fluid dark matter (PFDM) backgrounds, incorporating quantum corrections through the Generalized Uncertainty Principle (GUP) and Zitterbewegung oscillations. Starting from an action combining Einstein gravity, Maxwell electromagnetism, non-Abelian YM fields, and PFDM, we derive static spherically symmetric solutions with metric function <math altimg='si27.svg'><mrow><mi>f</mi><mrow><mo>(</mo><mi>r</mi><mo>)</mo></mrow><mo linebreak='goodbreak'>=</mo><mn>1</mn><mo linebreak='goodbreak'>&#8722;</mo><mn>2</mn><mi>M</mi><mo linebreak='goodbreak'>/</mo><mi>r</mi><mo linebreak='goodbreak'>+</mo><msup><mi>Q</mi><mn>2</mn></msup><mo linebreak='goodbreak'>/</mo><msup><mi>r</mi><mn>2</mn></msup><mo linebreak='goodbreak'>+</mo><msub><mi>Q</mi><mtext>YM</mtext></msub><mo linebreak='goodbreak'>/</mo><msup><mi>r</mi><mrow><mn>4</mn><mi>p</mi><mo>&#8722;</mo><mn>2</mn></mrow></msup><mo linebreak='goodbreak'>+</mo><mrow><mo>(</mo><mi>&#945;</mi><mo linebreak='badbreak'>/</mo><mi>r</mi><mo>)</mo></mrow><mi>ln</mi><mrow><mo>(</mo><mi>r</mi><mo linebreak='badbreak'>/</mo><mo>|</mo><mi>&#945;</mi><mo>|</mo><mo>)</mo></mrow></mrow></math>, where <italic>p</italic> controls YM self-interactions and <italic>&#945;</italic> governs dark matter coupling. Applying the Wentzel-Kramers-Brillouin (WKB) tunneling formalism, we compute spin-dependent Hawking temperatures, finding that higher-spin channels dominate emission, and GUP effects stabilize Planck-scale remnants. Exponential entropy corrections <math altimg='si28.svg'><mrow><msub><mi>S</mi><mi>C</mi></msub><mo linebreak='goodbreak'>=</mo><msub><mi>S</mi><mn>0</mn></msub><mo linebreak='goodbreak'>+</mo><msup><mi>e</mi><mrow><mo>&#8722;</mo><msub><mi>S</mi><mn>0</mn></msub></mrow></msup></mrow></math> yield quantum-modified thermodynamic potentials exhibiting phase transitions, while Joule-Thomson analysis reveals intricate cooling-heating regimes with multiple inversion curves. Keplerian frequency calculations demonstrate how YM charges and PFDM shift the innermost stable circular orbit (ISCO), and photon sphere analysis in dispersive plasma determines frequency-dependent shadow radii.

Türkiye

İzzet Sakallı

Yusuf Sucu

Erdem Sucu

Zitterbewegung oscillations and GUP-induced quantum modifications of Yang-Mills black holes in perfect fluid dark matter

<p>Using the recent six loop renormalization group functions for Lee-Yang and percolation theory constructed by Schnetz from a scalar cubic Lagrangian, we deduce the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ε</mi></math> expansion of the critical exponents for both cases. Estimates for the exponents in three, four, and five dimensions are extracted using two-sided Padé approximants and shown to be compatible with values from other approaches.</p>

J.A. Gracey

Six loop critical exponent analysis for Lee-Yang and percolation theory