We investigate the deformed Schur index in four dimensional $$\mathcal{N}=4$$ super Yang-Mills theories with $\textit{SO}$ and $\textit{Sp}$ gauge groups, generalizing Hatsuda’s recent calculations. We express the deformed Schur index as integrals of Koornwinder polynomials and Macdonald polynomials, then perform the integrals in terms of the normalization constants of Macdonald polynomials. We provide explicit results for some low rank gauge groups and for expansion in a $\textit{u}$ parameter. We discuss various special limits and the tests of S-duality.

China

Gao-fu Ren

Min-xin Huang

Deformed Schur indices of $\textit{BCD}$-type for $$\mathcal{N}=4$$ super Yang-Mills and symmetric functions

In the present paper we consider the usage of associative Yang-Baxter equations in the theory of classical and quantum <italic>ABCD</italic> algebras [1]. Classical and quantum associative analogs of the generalized Fredel-Maillet equations for <italic>ABCD</italic> tensors [2, 3] are found. Two classes of examples &#8212; rational and trigonometric &#8212; of classical and quantum <italic>ABCD</italic> tensors satisfying these equations are considered in details.

Ukraine

T. Skrypnyk

On ABCD algebras and associative Yang-Baxter equations

In the phenomenological study of dark photon, its mass origin is usually not of concern. However, in theoretical model construction, its mass is often generated via a dark Higgs mechanism, which leads to the presence of a light (non-decoupled) dark Higgs particle. In this work, we study the impact of such a dark Higgs particle on the collider detection of the dark photon. We focus on the process of final state dark photon radiating dark Higgs, which is called dark final state radiation (FSR). Considering the effects on both the signal cross section and the distribution of the squared missing mass, the invisible dark photon search at BaBar is reanalyzed and a new exclusion limit for invisible dark photon is presented.

Song Li

Jin Yang

Mengchao Zhang

Yang Zhang

Rui Zhu

Unraveling dark Higgs mechanism via dark photon production at an $\textit{e}$

I present a large-$\textit{N}$ determination of the topological susceptibility $\textit{χ}$ of SU($\textit{N}$) Yang-Mills theories using non-perturbative numerical Monte Carlo simulations of the lattice-discretized theory for 3 ≤ $\textit{N}$ ≤ 6, and adopting the Parallel Tempering on Boundary Conditions (PTBC) algorithm to bypass topological freezing for $\textit{N >}$ 3. Thanks to this algorithm I am able to explore a uniform range of lattice spacings across all values of $\textit{N}$, and to precisely determine $\textit{χ}$ for finer lattice spacings compared to previous studies with periodic or open boundary conditions. By taking the continuum limit at fixed smoothing radius in physical units, I am also able to show the independence of the continuum limit of $\textit{χ}$ from this choice. I conclude providing a comprehensive comparison of my new PTBC results with previous determinations of the topological susceptibility in the literature, both at finite $\textit{N}$ and in the large-$\textit{N}$ limit.

Spain

Claudio Bonanno

The large-$\textit{N}$ limit of the topological susceptibility of SU($\textit{N}$) Yang-Mills theories via Parallel Tempering on Boundary Conditions

We determine the four-point correlation function and amplitude in planar, maximally supersymmetric Yang-Mills theory to 12 loops. We find that the recently introduced “double-triangle” rule in fact implies the previously described square and pentagon rules; and when applied to 12 loops, it fully determines the 11-loop correlator and fixes all but 3 of the (619,981,403) 12-loop coefficients; these remaining coefficients can be subsequently fixed using the “(single-)triangle” rule. Not only do we confirm the Catalan conjecture for antiprism graphs, but we discover evidence for a greatly generalized Catalan conjecture for the coefficients of all polygon-framed fishnet graphs. We provide all contributions through 12 loops as Supplemental Material to this work.

United States

Jacob L. Bourjaily

Song He

Canxin Shi

Yichao Tang

Four-point correlator of planar supersymmetric Yang-Mills theory at twelve loops

We develop a machine learning assisted holographic model that consistently describes both the equation of state and glueball spectrum of pure Yang-Mills theory, achieved through neural network reconstruction of Einstein-dilaton gravity. Our framework incorporates key nonperturbative constraints of lattice QCD data: The ground (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>0</mn><mrow><mo>+</mo><mo>+</mo></mrow></msup></math>) and first-excited (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>0</mn><mrow><mo>+</mo><mo>+</mo><mo>*</mo></mrow></msup></math>) scalar glueball masses pins down the infrared (IR) geometry, while entropy density data anchors the ultraviolet (UV) behavior of the metric. A multistage neural network optimization then yields the full gravitational dual—warp factor <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>A</mi><mo stretchy="false">(</mo><mi>z</mi><mo stretchy="false">)</mo></math> and dilaton field <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Φ</mi><mo stretchy="false">(</mo><mi>z</mi><mo stretchy="false">)</mo></math>—that satisfies both spectroscopic and thermodynamic constraints. The resulting model accurately reproduces the deconfinement phase transition thermodynamics (pressure, energy density, trace anomaly) and predicts higher glueball excitations (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>0</mn><mrow><mo>+</mo><mo>+</mo><mo>*</mo><mo>*</mo></mrow></msup></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>0</mn><mrow><mo>+</mo><mo>+</mo><mo>*</mo><mo>*</mo><mo>*</mo></mrow></msup></math>) consistent with available lattice calculations. This work establishes a new paradigm for data-driven holographic reconstruction, solving the long-standing challenge of unified description of confinement thermodynamics and spectroscopy.

Italy

Xun Chen

Yidian Chen

Kai Zhou

Data-driven Einstein-dilaton model for pure Yang-Mills thermodynamics and glueball spectrum

We investigate the influence of a constant magnetic field on the screening length of a heavy quarkonium propagating through a strongly coupled $$\mathcal {N}=4$$ super Yang–Mills plasma. Our analysis is conducted by evaluating the Wilson loop in a boosted magnetic brane background, with additional consideration of quarkonia axes aligned along different directions. We find that the presence of a magnetic field reduces the screening length, which in turn lowers the quarkonium binding energy. Moreover, the inclusion of a magnetic field enhances quarkonium dissociation, a result that is consistent with prior observations regarding the entropic force and imaginary potential.

Ping-ping Wu

Zi-qiang Zhang

Xiangrong Zhu

Screening length of heavy quarkonia moving through a strongly coupled $$\mathcal {N}=4$$ super Yang–Mills plasma in a magnetic field

Working in a sector of large charge is a powerful tool to analytically access models that are either strongly coupled or otherwise difficult to solve explicitly. In the context of integrable systems, Volin’s method is exactly such a large-charge approach. In this note, we apply this method to the bi-Yang-Baxter deformed <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>2</mn><mo stretchy="false">)</mo></math> principal chiral model. Our main result is an explicit expression for the free energy density as an asymptotic expansion. We moreover determine the leading nonperturbative effects both via analytic methods and a resurgence analysis.

Switzerland

Meer Ashwinkumar

Japan

Domenico Orlando

Susanne Reffert

Giacomo Sberveglieri

Asymptotics in the bi-Yang-Baxter sigma model

We investigate elliptical Wilson loops in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">N</mi><mo>=</mo><mn>4</mn></math> Super Yang–Mills theory at weak and strong coupling for small values of the eccentricity. We obtain analytical results for the vacuum expectation value of the Wilson loop in the form of a series in the eccentricity parameter. At weak coupling, we use perturbation theory in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">N</mi><mo>=</mo><mn>4</mn></math> Super Yang–Mills. At strong coupling, we use the AdS/CFT correspondence, which maps the Wilson loop to the minimal-area world sheet of an open string in anti–de Sitter (AdS) space. We present a novel perturbative method to solve the Nambu–Goto equations allowing us to describe the minimal surface in terms of a coordinate parametrization in Euclidean <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>AdS</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></math>. Our results for the regularized area agree with those obtained by Dekel [<a href="http://dx.doi.org/10.1007/JHEP03(2015)085">J. High Energy Phys. 03 (2015) 085</a>.] based on the Polyakov action.

Brazil

Czechia

Thales Azevedo

Alfonso Ballon-Bayona

Leonardo Pazito

Elliptical Wilson loops in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">N</mi><mo>=</mo><mn>4</mn></math> Super Yang-Mills theory

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