Since the inception of lattice QCD, a natural definition for the Yang-Mills instanton on lattice has been long sought for. In a recent work [1], one of authors showed the natural solution has to be organized in terms of bundle gerbes in higher homotopy theory / higher category theory, and introduced the principles for such a categorical construction. To pave the way towards actual numerical implementation in the near future, nonetheless, an explicit construction is necessary. In this paper we provide such an explicit construction for SU(2) gauge theory, with technical aspects inspired by Lüscher’s 1982 geometrical construction [2]. We will see how the latter is in a suitable sense a saddle point approximation to the full categorical construction. The generalization to SU($\textit{N}$) will be discussed. The construction also allows for a natural definition of lattice Chern-Simons-Yang-Mills theory in three spacetime dimensions.

China

Peng Zhang

Jing-Yuan Chen

An explicit categorical construction of instanton density in lattice Yang-Mills theory

Recently, an exact black hole solution in non-minimal Einstein–Yang–Mills theory was obtained, and its quasinormal modes were subsequently analyzed using the JWKB approximation (Gogoi and Ponglertsakul in Eur. Phys. J. C 84:652, 2024. . [gr-qc]). However, we demonstrate that this analysis lacks sufficient accuracy when studying modes with $$\ell \le n$$ , where $$\ell $$ is the multipole number and $\textit{n}$ is the overtone number. To address this, we compute the quasinormal frequencies using the precise Leaver method. Our results show that while the fundamental mode deviates only slightly from the Schwarzschild value, the first few overtones exhibit significantly larger deviations, with the discrepancy growing rapidly with the overtone number. Moreover, beginning with the second overtone, we observe a striking phenomenon: the real part of the frequency tends to zero quickly as the non-minimal coupling constant increases. This combination of spectral stability in the fundamental mode and high sensitivity of the overtones suggests that the Yang–Mills contribution primarily deforms the metric in the near-horizon region, while the geometry quickly transitions back to a Schwarzschild-like form at larger radii. In addition, we compute the grey-body factors and confirm that they represent a more stable characteristic of the geometry, exhibiting a correspondence with quasinormal modes already at the first multipole. The Yang–Mills coupling enhances the grey-body factors, further increasing the transmission probability.

Czechia

B. Lütfüoğlu

Non-minimal Einstein–Yang–Mills black holes: fundamental quasinormal mode and grey-body factors versus outburst of overtones

Using the AdS/CFT correspondence, we investigate the holographic image of an AdS black hole in Einstein-power-Yang-Mills gravity. The AdS boundary hosts a Gaussian oscillation source, which induces a lensed response on the opposite side of the boundary during propagation through bulk spacetime. The optical system enables observers at the north pole to continuously capture holographic images that exhibit an axisymmetric bright ring known as the Einstein ring. As the observation position shifts, the bright ring gradually transforms into a luminous arc and eventually transitions into a light point. Additionally, we examine the impact of variations in relevant physical quantities on the ring and present the corresponding brightness curve. The results indicate that, as the temperature $\textit{T}$ and nonlinear Yang Mills charge parameter $\textit{q}$ increase, the ring radius increases, whereas an increase in chemical potential $\textit{u}$ leads to a decrease in ring radius. However, the peak brightness curve of the ring invariably decreases as the values of $\textit{T}$, $\textit{u}$, and $\textit{q}$ increase, albeit to varying degrees. Comparing the outcomes of geometric optics, we observe that the position of the ring in holography images is consistent with that of the photon ring.

Xin-Yun Hu

Ke-Jian He

Xiao-Xiong Zeng

Holographic image features of an AdS black hole in Einstein-power-Yang-Mills gravity * Supported by the National Natural Science Foundation (11875095), the Innovation and Development Joint Foundation of Chongqing Natural Science Foundation (CSTB2022NSCQ-LZX0021), the Basic Research Project of Science and Technology Committee of Chongqing, China (CSTB2023NSCQ-MSX0324), and the Natural Science Foundation of Chongqing, China (CSTB2023NSCQ-MSX0594)

We combine the Yang-Baxter (YB) and bi-Yang-Baxter (bi-YB) deformations with higher-spin auxiliary field deformations to construct multi-parameter families of integrable deformations of the principal chiral model on a Lie group $\textit{G}$ with semi-simple Lie algebra $$ \mathfrak{g} $$ . In the YB case, our construction produces one integrable deformation for each pair ( $$ \mathcal{R} $$ $\textit{, E}$), where $$ \mathcal{R} $$ is an antisymmetric bilinear operator on $$ \mathfrak{g} $$ obeying the modified classical Yang-Baxter equation and $\textit{E}$ is a function of several variables. In the bi-YB case, the pair becomes a triplet ( $$ \mathcal{R} $$ $\textit{,}$ $$ \overset{\sim }{\mathcal{R}} $$ $\textit{, E}$), where $$ \overset{\sim }{\mathcal{R}} $$ is another antisymmetric bilinear operator on $$ \mathfrak{g} $$ obeying the modified classical Yang-Baxter equation. We show that every model in these families is (weakly) classically integrable by exhibiting a Lax representation for their equations of motion.

Thailand

Daniele Bielli

United States

Christian Ferko

Australia

Liam Smith

Gabriele Tartaglino-Mazzucchelli

Auxiliary field sigma models and Yang-Baxter deformations

<p>In this work, we investigated the off-shell expansion relation of the Yang-Mills scalar theory. We explicitly showed that the single-trace Berends-Giele currents in the Yang-Mills scalar theory can be decomposed into a term expressed by a linear combination of bi-adjoint scalar Berends-Giele currents and one that vanishes under the on-shell limit. We proved that the bi-adjoint scalar currents, as well as the corresponding coefficients, can be characterized by a graphic approach that was originally studied in the Einstein-Yang-Mills expansion. Furthermore, we generalized the decomposition to the multitrace case through unifying relations and established the connection both in single-trace and multitrace graphic descriptions. Finally, we established the relations between the Yang-Mills currents and the single-trace Yang-Mills scalar currents, choosing special reference orders of the Yang-Mills graphs.</p>

Yi-Xiao Tao

Germany

Konglong Wu

Off-shell expansion relation of the Yang-Mills scalar theory

We construct invertible spectral parameter dependent Yang-Baxter solutions ($\textit{R}$-matrices) by Baxterizing constant non-invertible Yang-Baxter solutions. The solutions are algebraic (representation independent). They are constructed using supersymmetry (SUSY) algebras. The resulting $\textit{R}$-matrices are regular leading to local non-hermitian Hamiltonians written in terms of the SUSY generators. As particular examples we Baxterize the 4 × 4 constant non-invertible solutions of Hietarinta leading to nearest-neighbor Hamiltonians. On comparing with the literature we find that two of the models are new. Apart from being non-hermitian, many of them are also non-diagonalizable with interesting spectrums. With appropriate representations of the SUSY generators we obtain spin chains in all local Hilbert space dimensions.

India

Somnath Maity

Pramod Padmanabhan

Vladimir Korepin

Non-hermitian integrable systems from constant non-invertible solutions of the Yang-Baxter equation

We study $$ \mathcal{N} $$ = 1 SU($\textit{N}$) super Yang-Mills (SYM) theory on $\textit{ℝ}$ × ($\textit{S}$ ) × ($\textit{S}$ ) with the ’t Hooft twist. The theory becomes weakly coupled if the length $\textit{L}$ of ($\textit{S}$ ) is sufficiently small, $\textit{NL}$ Λ ≪ 1. We explore the nonperturbative dynamics at the weak-coupling regime by changing the size of $\textit{L}$ and uncover how 3d monopole/bion-based effective theory for $\textit{L}$ ≫ $\textit{L}$ is related to the 2d vortex-based theory for $\textit{L}$ ≈ $\textit{L}$ . The highlights of our results are (1) the smooth “weak-weak” continuity of the vacuum structure and gluino condensate during the 3d-2d dimensional reduction, (2) the switching of Wilson loop behavior from the area law in 3d to the perimeter law in 2d via a “double-string” picture, (3) the role of mass deformation in breaking discrete chiral symmetry and restoring the area law in 2d, and (4) the microscopic investigation of bions during the reduction from 3d to 2d and the cancellation of the vacuum energy due to the hidden topological angle. We also discuss the generalization of our results for (1)–(3) from $$ \mathcal{N} $$ = 1 SYM to QCD with adjoint quarks.

Japan

Yui Hayashi

Tatsuhiro Misumi

Yuya Tanizaki

Monopole-vortex continuity of $$ \mathcal{N} $$ = 1 super Yang-Mills theory on $\textit{ℝ}$

We start from the classical Kadomtsev-Petviashvili (KP) hierarchy posed on formal pseudo-differential operators, and we produce new hierarchies of non-linear equations in the context of non-formal pseudo-differential operators lying in the Kontsevich and Vishik's odd class. In particular, we show that it is possible to <italic>lift</italic> the standard KP hierarchy to hierarchies of differential equations for non-formal pseudo-differential operators, and to recover the former starting from the latter. We prove that the corresponding Zakharov-Shabat equations hold in this context, and we express one of our hierarchies as the minimization of a class of Yang-Mills action functionals on a space of pseudo-differential connections whose curvature takes values in the Dixmier ideal. We finish by comparing our Kadomtsev-Petviashvili hierarchies in terms of the kind of solutions that they produce for the KP-II equation.

France

Slovakia

Jean-Pierre Magnot

Chile

Enrique G. Reyes

Kadomtsev-Petviashvili hierarchies with non-formal pseudo-differential operators, non-formal solutions, and a Yang-Mills–like formulation

Quantum knot invariants (like colored HOMFLY-PT or Kauffman polynomials) are a distinguished class of non-perturbative topological invariants. Any known way to construct them (via Chern-Simons theory or quantum R-matrix) starts with a finite simple Lie algebra. Another set of knot invariants – of finite type – is related to quantum invariants via a perturbative expansion. However can all finite type invariants be obtained in this way? Investigating this problem, P. Vogel discovered a way to polynomially parameterize the expansion coefficients with three parameters so that, at different specific values, this reproduces the answers for all simple Lie (super)algebras. Then it is easy to construct a polynomial <math altimg='si1.svg'><msub><mrow><mi>P</mi></mrow><mrow><mi>a</mi><mi>l</mi><mi>g</mi></mrow></msub></math> that vanishes for all simple Lie algebras, and the corresponding Vassiliev invariant would thus be absent from the perturbative expansion.

Russia

D. Khudoteplov

A. Morozov

A. Sleptsov

Can Yang-Baxter imply Lie algebra?

We carry out a hybrid Monte Carlo (HMC) simulation of the <inline-formula><tex-math id='TM0002' notation='LaTeX'>$SU(2)/\mathbb {Z}_2$</tex-math></inline-formula> Yang&#8211;Mills theory in which the <inline-formula><tex-math id='TM0003' notation='LaTeX'>$\mathbb {Z}_N$</tex-math></inline-formula> 2-form flat gauge field (the &#8217;t&#160;Hooft flux) is explicitly treated as one of the dynamical variables. We observe that our HMC algorithm in the <inline-formula><tex-math id='TM0004' notation='LaTeX'>$SU(2)/\mathbb {Z}_2$</tex-math></inline-formula> theory drastically reduces autocorrelation lengths of the topological charge and of a physical quantity which couples to slow modes in the conventional HMC simulation of the <inline-formula><tex-math id='TM0005' notation='LaTeX'>$SU(2)$</tex-math></inline-formula> theory. Provided that sufficiently large lattice volumes are available, therefore, the HMC algorithm of the <inline-formula><tex-math id='TM0006' notation='LaTeX'>$SU(N)/\mathbb {Z}_N$</tex-math></inline-formula> theory could be employed as an alternative for the simulation of the <inline-formula><tex-math id='TM0007' notation='LaTeX'>$SU(N)$</tex-math></inline-formula> Yang&#8211;Mills theory, because local observables are expected to be insensitive to the difference between <inline-formula><tex-math id='TM0008' notation='LaTeX'>$SU(N)$</tex-math></inline-formula> and&#160; <inline-formula><tex-math id='TM0009' notation='LaTeX'>$SU(N)/\mathbb {Z}_N$</tex-math></inline-formula> in the large volume limit. A possible method to incorporate quarks [fermions in the fundamental representation of&#160; <inline-formula><tex-math id='TM0010' notation='LaTeX'>$SU(N)$</tex-math></inline-formula> with the baryon number&#160; <inline-formula><tex-math id='TM0011' notation='LaTeX'>$1/N$</tex-math></inline-formula>] in this framework is also considered.

Motokazu Abe

Okuto Morikawa

Hiroshi Suzuki

Monte Carlo Simulation of the <italic>SU</italic>(2)/&#8484; <sub>2</sub> Yang&#8211;Mills Theory