We set the scale of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>SU</mi><mo stretchy="false">(</mo><mi>N</mi><mo stretchy="false">)</mo></mrow></math> Yang-Mills theories for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi><mo>=</mo><mn>3</mn></math>, 5, 8 and in the large-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math> limit via gradient flow, as a first step towards the computation of the large-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math> <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Λ</mi></math>-parameter using step scaling. We adopt twisted boundary conditions to achieve large-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math> volume reduction and the Parallel Tempering on Boundary Conditions algorithm to tame topological freezing. This setup allows accurate determinations of the gradient-flow scales down to lattice spacings as fine as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>∼</mo><mn>0.025</mn><mtext> </mtext><mtext> </mtext><mi>fm</mi></math> for all the explored values of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math>, a regime that has never been reached with ergodic algorithms. Moreover, we are able to precisely estimate the finite-size systematics related to topological freezing, and to show the suppression of finite-volume effects expected by virtue of large-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math> twisted volume reduction.

Claudio Bonanno

Jorge Luis Dasilva Golán

Margarita García Pérez

Massimo D’Elia

Andrea Giorgieri

Scale setting of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>SU</mi><mo stretchy="false">(</mo><mi>N</mi><mo stretchy="false">)</mo></mrow></math> Yang–Mills theory, topology and large-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math> volume independence

We investigate the dynamics of four-dimensional $$ \mathcal{N}=2 $$ SU(2) super Yang-Mills theory on an AdS background. We propose that the boundary conditions that preserve the AdS super-isometries are determined by maximizing the real part of the AdS partition function $\textit{F}$ = −log $\textit{Z}$ . At weak coupling Λ$\textit{L}$ ≪ 1 the maximization singles out the Dirichlet boundary condition with an SU(2) boundary global symmetry, corresponding to the classical vacuum at the origin of the Coulomb branch with fully un-higgsed gauge group. We find that for Λ$\textit{L}$ ~ 𝒪(1) new boundary conditions are favored, with gauge-group higgsed down to U(1), matching the expectation from the flat space limit. We use supersymmetric localization to compute $\textit{Z}$ nonperturbatively. We further provide evidence for a relation between $\textit{F}$ and the $$ \mathcal{N}=2 $$ prepotential in AdS background.

China

Davide Bason

United Kingdom

Christian Copetti

Italy

Lorenzo Pietro

United States

Ziming Ji

$$ \mathcal{N}=2 $$ super Yang-Mills in AdS4 and $\textit{F}$ AdS-maximization

We systematically classify all supersymmetry-preserving mass deformations of SYM matrix models in all dimensions ($\textit{D}$ = 3, 4, 6, 10). In $\textit{D}$ = 10, the polarized IKKT model emerges as the only possible deformation. In $\textit{D}$ = 4, we identify two massive models without a sign problem, making them attractive candidates for non-perturbative numerical studies.

Switzerland

Adrien Martina

Massive deformations of supersymmetric Yang-Mills matrix models

We derive the explicit formula for fractional BPS lumps (or fractional instantons) in the $\textit{ℂP}$ nonlinear sigma model on a two-dimensional torus under various shift-clock twisted boundary conditions. After regularizing the $\textit{ℂP}$ model by an $\textit{N}$-component Abelian-Higgs model, those twisted boundary conditions introduce nontrivial ’t Hooft fluxes $\textit{p}$/$\textit{N}$ for the U(1) gauge field, and the topological charge becomes fractionalized as $\textit{k}$ + $\textit{p}$/$\textit{N}$ ∈ $\textit{ℤ}$ + $\textit{p}$/$\textit{N}$. The moduli space is globally determined as the $\textit{ℂP}$ -fiber bundle on a 2-torus, which is a Kähler manifold of complex dimension $\textit{Nk}$ + $\textit{p}$ as predicted by the index theorem. We present two different parametrizations of the moduli space: one of them immediately identifies the small-lump singularity appearing in the $\textit{ℂP}$ limit, while the other makes the modular invariance manifest.

Japan

Yui Hayashi

Tatsuhiro Misumi

Muneto Nitta

Keisuke Ohashi

Yuya Tanizaki

Fractional instantons in 2d $\textit{ℂP}$ $\textit{N}$ − 1 model and 4d Yang-Mills theory with ’t Hooft twists

We present a high-precision study of the topological susceptibility in SU(3) pure gauge theory in four space-time dimensions. The result is based on ensembles at seven lattice spacings and in seven physical volumes to facilitate a controlled continuum and infinite-volume extrapolation. We use a gluonic topological charge measurement, with gradient flow smoothing in the operator. Two complementary smoothing strategies are used (one keeps the flow time fixed in lattice units, one in physical units). Our data support the idea that both strategies yield a universal continuum limit; we find <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>χ</mi></mrow><mrow><mi>top</mi></mrow><mrow><mn>1</mn><mo>/</mo><mn>4</mn></mrow></msubsup><msub><mrow><mi>r</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>=</mo><mn>0.4775</mn><mo stretchy="false">(</mo><mn>14</mn><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mn>11</mn><mo stretchy="false">)</mo></mrow></math> or <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>χ</mi><mi>top</mi><mrow><mn>1</mn><mo>/</mo><mn>4</mn></mrow></msubsup><mo>=</mo><mn>198.1</mn><mo stretchy="false">(</mo><mn>0.7</mn><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mn>2.7</mn><mo stretchy="false">)</mo><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>. Our Appendix data suggest that the excess kurtosis <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">⟨</mo><msup><mi>q</mi><mn>4</mn></msup><mo stretchy="false">⟩</mo><mo>/</mo><mo stretchy="false">⟨</mo><msup><mi>q</mi><mn>2</mn></msup><msup><mo stretchy="false">⟩</mo><mn>2</mn></msup><mo>−</mo><mn>3</mn></math> decreases <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>∝</mo><msup><mi>L</mi><mrow><mo>−</mo><mn>2</mn></mrow></msup></math> for large box sizes <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>L</mi></math>.

Germany

Stephan Dürr

Gianluca Fuwa

Topological susceptibility and excess kurtosis in SU(3) Yang-Mills theory

We continue to explore the previously suggested dual regime of Yang-Baxter (YB) deformed <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">O</mi><mo stretchy="false">(</mo><mn>2</mn><mi>N</mi><mo stretchy="false">)</mo></math> sigma models, which is a new one-parametric deformation of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">O</mi><mo stretchy="false">(</mo><mn>2</mn><mi>N</mi><mo stretchy="false">)</mo></math> model. It can be obtained from the conventional YB deformed <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">O</mi><mo stretchy="false">(</mo><mn>2</mn><mi>N</mi><mo>+</mo><mn>2</mn><mo stretchy="false">)</mo></math> sigma model by freezing two isometries. The scattering matrix in the nondeformed <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">O</mi><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">)</mo></math> model is known to coincide with the rational <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mrow><mi mathvariant="fraktur">so</mi></mrow><mi>n</mi></msub></math>-invariant <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>R</mi></math>-matrix. For <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>n</mi><mo>=</mo><mn>2</mn><mi>N</mi></math> this rational solution allows for two trigonometric deformations: the usual <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mi>N</mi><mrow><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></mrow></msubsup></math> and the twisted <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mi>N</mi><mrow><mo stretchy="false">(</mo><mn>2</mn><mo stretchy="false">)</mo></mrow></msubsup></math>. The usual one is known to coincide with the scattering matrix of the conventional YB-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">O</mi><mo stretchy="false">(</mo><mn>2</mn><mi>N</mi><mo stretchy="false">)</mo></math> model. A natural question to ask is what sigma model corresponds to the twisted solution. In this work we claim that it is precisely our dual regime of YB-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">O</mi><mo stretchy="false">(</mo><mn>2</mn><mi>N</mi><mo stretchy="false">)</mo></math>. We find the corresponding unitarizing function <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>F</mi><mi>N</mi></msub><mo stretchy="false">(</mo><mi>θ</mi><mo stretchy="false">)</mo></math> explicitly, and, as a bonus, extract some physical properties of this system using the thermodynamic Bethe ansatz technique.

Russia

Alexey Bychkov

Boris Nekrasov

Scattering in the dual regime of Yang-Baxter deformed <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="normal">O</mi><mo stretchy="false">(</mo><mn>2</mn><mi>N</mi><mo stretchy="false">)</mo></mrow></math> sigma models

Several possible excesses around $ 95 $ GeV hint at an additional light scalar beyond the Standard Model. We examine the capability of the Circular Electron-Positron Collider (CEPC) to test this hypothesis in the Higgs-strahlung channel $ e^{+}e^{-} \to ZS $ with $ Z \to\mu^{+}\mu^{-} $ and $ S \to\tau^{+}\tau^{-} $ . A full detector simulation shows that the optimal center-of-mass energy for studying the 95 GeV light scalar is 210 GeV. A deep neural network classifier reduces the luminosity required for discovery by half. At $ L = 20\; \mathrm{ab}^{-1} $ , the $ 5\sigma $ sensitivity of the CEPC to the signal strength $ \mu_{\tau\tau}^{ZS} $ reaches 0.016 and 0.020 for $ \sqrt{s} = 210 $ GeV and 240 GeV, respectively. The corresponding thresholds for a 5% precision measurement are $ \mu_{\tau\tau}^{ZS} \gt 0.10 $ and $ \gt 0.12 $ . At $ \sqrt{s}=210 $ GeV (240 GeV), the $ 5\sigma $ coverage of all N2HDM-Flipped samples with $ \chi^2_{h_{95}} \lt 7.82 $ requires $ L=800\ \mathrm{fb}^{-1} $ (1.22 $ \mathrm{ab}^{-1} $ ). These results establish a 210 GeV run, augmented by machine-learning selection, as the most efficient strategy to confirm or refute the 95 GeV excess at future lepton colliders.

Yabo Dong

Manqi Ruan

Kun Wang

Haijun Yang

Jingya Zhu

Testing a 95 GeV Scalar at the CEPC with Machine Learning * This work was supported by the National Natural Science Foundation of China under Grant No. 12275066 and by the startup research funds of Henan University. The work of K. Wang was also supported by the Open Project of the Shanghai Key Laboratory of Particle Physics and Cosmology under Grant No. 22DZ2229013-3. The work of M. Ruan was also supported by the National Key Program for S&T Research and Development under Contract No. 2024YFA1610603. The work of H. Yang was also supported by the National Natural Science Foundation of China under Grant No. W2441004.

We propose an <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>AdS</mi><mo>×</mo><mi mathvariant="normal">S</mi></mrow></math> factorization formula at the level of the generating function for correlators with arbitrary Kaluza-Klein configurations and implement it in the supergravity limit of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">N</mi><mo>=</mo><mn>4</mn></mrow></math> supersymmetric Yang-Mills theory. By incorporating this mechanism into Mellin space bootstrap, together with an observed <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>Z</mi><mn>2</mn></msub></math> symmetry under <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>AdS</mi><mo stretchy="false">↔</mo><mi mathvariant="normal">S</mi></mrow></math>, we manage to simultaneously work out unified formulas both for all five-point half-BPS correlators and for all four-point correlators with one superdescendant. This <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>AdS</mi><mo>×</mo><mi mathvariant="normal">S</mi></mrow></math> bootstrap method is directly applicable to generic multipoint computation at tree level.

Portugal

Bruno Fernandes

Vasco Gonçalves

Zhongjie Huang

Yichao Tang

Joao Vilas Boas

Ellis Ye Yuan

<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>AdS</mi><mo stretchy="false">×</mo><mi mathvariant="normal">S</mi></mrow></math> Mellin Bootstrap, Hidden 10D Symmetry and Five-Point Kaluza-Klein Functions in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">N</mi><mo>=</mo><mn>4</mn></mrow></math> Supersymmetric Yang-Mills Theory

We study the algebraic structure of one-loop Bern-Carrasco-Johansson numerators in Yang-Mills and related theories. Starting from the propagator matrix that connects color-ordered integrands to numerators, we identify the consistency conditions that ensure the existence of Jacobi-satisfying numerator solutions and determine the unique construction. The relation between one-loop numerators and forward-limit tree numerators is clarified, together with the additional physical conditions required for a consistent double-copy interpretation. We propose a two-step expansion strategy for obtaining explicit one-loop numerators. The Yang-Mills integrand is first decomposed into scalar-loop Yang-Mills-scalar building blocks, which are then expanded into biadjoint scalar integrands. We derive explicit results for up to three external gluons, showing how the kinematic consistency conditions uniquely determine the coefficients in each case. Similar results for Einstein-Yang-Mills and gravity amplitudes are also presented.

Yi-Jian Du

Chih-Hao Fu

Yihong Wang

Chongsi Xie

Algebraic consistency and explicit construction of one-loop Bern-Carrasco-Johansson numerators of Yang-Mills and related theories

We investigate the quantum properties of the truly gauge-invariant and conserved charges of two-dimensional Yang-Mills theories, focusing on lattice QCD in the strong coupling regime. The construction of those charges uses the integral version of the (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>1</mn><mo>+</mo><mn>1</mn></mrow></math>)-dimensional Yang-Mills equations, and they correspond to the eigenvalues of a charge operator. The gauge invariance of the charges suggests that they are not confined, hence hadronic states may carry them. Using the path integral formalism with imaginary time (Euclidean), we evaluate the correlation functions of those charges on baryon and meson states through functional integrals over the gauge group <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mi>N</mi><mo stretchy="false">)</mo></math> (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi><mo>=</mo><mn>2</mn></math>, 3) and Grassmannian variables—the fermionic fields. Our results show that the expectation values of the lowest nontrivial charges are nonzero for baryon and meson states but vanish for non-gauge-invariant states, supporting the interpretation that hadrons indeed carry these charges. While renormalization effects and higher-order contributions remain to be analyzed, these findings point toward a potential link between gauge-invariant charges and confinement.

Brazil

Paulo A. Faria da Veiga

Luiz A. Ferreira

Henrique Malavazzi

Ravi Mistry

Quantum Yang-Mills charges in strongly coupled <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2</mn><mi>D</mi></math> lattice QCD with three flavors