We compute the complete nonplanar integrand for the correlation function of four lightest scalar operators 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 five-loop order. This is equivalent to the supercorrelator of nine stress-tensor multiplets in the self-dual theory. Starting with an ansatz of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>f</mi></math> graphs, we impose constraints from light-cone limits, and fix the remaining freedom by using the reformulation of the theory in twistor space. We develop an efficient GPU-based algorithm for the numerical evaluation of the twistor rules. Our result for the integrand suggests a sharpened <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>f</mi></math>-graph genus conjecture. As an application, we extract the five-loop nonplanar anomalous dimension of the Konishi operator, whose <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mo>/</mo><msubsup><mi>N</mi><mi mathvariant="normal">c</mi><mn>2</mn></msubsup></math> term is entirely given in terms of odd zeta values of transcendentality five and higher. Our code and result are provided in ancillary files.

Germany

Till Bargheer

Albert Bekov

Nonplanar four-point integrand and Konishi dimension 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> super-Yang-Mills theory at five loops

We derive a novel two-field four-dimensional integrable field theory (IFT) from 6D holomorphic Chern-Simons theory on twistor space. The four-dimensional IFT depends on a skew-symmetric linear operator acting on a Lie algebra, and when this operator is specialized to a solution of the modified classical Yang-Baxter equation, the IFT develops a semilocal symmetry associated with this solution. The resulting 4D analog of the Yang-Baxter sigma model is related by symmetry reduction to the well-known 2D Yang-Baxter sigma model. An important implication that we find is the embedding of the equations of motion of the 2D Yang-Baxter sigma model in the anti-self-dual Yang-Mills equations. The 6D Chern-Simons theory on twistor space can alternatively be symmetry reduced to a 4D Chern-Simons theory configuration with disorder surface defects. The latter realizes the Yang-Baxter sigma model, implying a “diamond” for the Yang-Baxter sigma model obtained from twistor space. We also show that the homogeneous 2D Yang-Baxter sigma model can be derived from a limit of our setup.

Switzerland

Meer Ashwinkumar

China

Jitendra Pal

Yang-Baxter sigma model from twistor space

The analytic structure of the partition function in finite-volume systems is investigated at complex chemical potentials in a minimal mean-field effective model of QCD with finite-size effects incorporated. We discuss the temperature dependence of the Lee-Yang zeros and their relation to the edge singularity for various system sizes. Different methods for locating the critical point based on finite-size scaling of Lee-Yang zeros and susceptibility ratios are compared. We demonstrate that these methods can successfully identify the critical point, whereas a careful treatment of corrections from irrelevant operators is crucial for its accurate determination.

Japan

Tatsuya Wada

Poland

Hungary

Győző Kovács

Masakiyo Kitazawa

Takahiro M. Doi

Lee-Yang zeros and edge singularity in a mean-field approach

In this work, we investigate the solutions to the governing equations of the Yang–Mills–Higgs model coupled with a dilaton. These solutions describe energy-minimizing static spherically symmetric field configurations with unit topological charge. We analyze the equations for different values of the Higgs self-coupling parameter <italic>&#946;</italic>. For any Higgs self-coupling parameter <italic>&#946;</italic>&#8239;&gt;&#8239;0, we use a regularization method to obtain the full set of boundary conditions. In the weak coupling limit <italic>&#946;</italic>&#8239;&#8594;&#8239;0, we derive the monotonicity of the solutions. In the limit <italic>&#946;</italic>&#8239;&#8594;&#8239;&#8734;, the governing system reduces to the equation governing a single dilaton field. We find that the Euler&#8211;Lagrange equation is equivalent to a first-order Bogomol&#8217;nyi&#8211;Prasad&#8211;Sommerfield (BPS) equation, which admits an explicit solution. Furthermore, for any <italic>&#946;</italic>&#8239;&gt;&#8239;0, we derive the energy bounds using the monotonicity of the energy function with respect to <italic>&#946;</italic> and calculate the magnetic charge.

Yin Liu

Shouxin Chen

Static spherically symmetric monopole solutions to the Yang–Mills–Higgs model coupled with a dilaton

We propose a bootstrap program for the $\textit{form factor squared}$ with operator tr($\textit{ϕ}$ ) in maximally supersymmetric Yang-Mills theory in the planar limit, which plays a central role for perturbative calculations of important physical observables such as energy correlators. The tree-level $\textit{N}$ -point form factor (FF) squared can be obtained by cutting $\textit{N}$ propagators of a collection of two-point “master diagrams” at ($\textit{N}$ – 1) loops: for $\textit{N}$ = 3, 4, 5, 6 there are merely 1, 2, 4, 13 topologies of such diagrams respectively, and their numerators are strongly constrained by power-counting (including “no triangle” property) and other constraints such as the “rung rule”. Moreover, these two-point diagrams provide a “unification” of FF squared at different numbers of loops and legs, which is similar to extracting (planar) amplitude squared from vacuum master diagrams (dual to $\textit{f}$ -graphs): by cutting 2 ≤ $\textit{n}$ < $\textit{N}$ propagators, one can also extract the planar integrand of $\textit{n}$-point FF squared at ($\textit{N}$ – $\textit{n}$) loops, thus our results automatically include integrands of 2-point (Sudakov) FF up to four loops (where the squaring is trivial), 3-point FF squared up to three loops, and so on. Our ansatz is completely fixed using soft limits of (tree and loop) FF squared and the multi-collinear limit which reduces it to the splitting function, without any other inputs such as unitarity cuts. This method opens up the exciting possibility of a $\textit{graphical bootstrap}$ for FF squared for higher $\textit{N}$ (which contains e.g. planar Sudakov FF to $\textit{N}$ – 2 loops) similar to that for the amplitude squared via $\textit{f}$ -graphs. We also comment on applications to the computation of leading order energy correlators where new structures are expected after performing phase-space integrations.

Song He

Xiang Li

Jingwen Lin

Jiahao Liu

Kai Yan

Bootstrapping form factor squared in $$ \mathcal{N} $$ = 4 super-Yang-Mills

As one of the key targets for future space-based gravitational wave detectors, extreme-mass-ratio inspirals (EMRIs) offer valuable observational clues for testing strong-field gravity and classifying black holes through their orbital dynamics and gravitational wave emission characteristics. This work systematically investigates the transitional periodic orbits of test particles and their single-cycle gravitational radiation features in the background of non-minimally coupled Einstein–Yang–Mills (EYM) BHs. The results show that as the magnetic charge parameter $$Q$$ and the non-minimal coupling constant $$\xi $$ increase, the radii of the marginally bound orbit ( $$r_{\text {MBO}}$$ ) and the innermost stable circular orbit ( $$r_{\text {ISCO}}$$ ) decrease significantly, with corresponding reductions in the orbital energy $$E$$ and angular momentum $$L$$ . Furthermore, the allowable parameter space of energy and angular momentum ( $$E$$ – $$L$$ ) for bound orbits shifts towards the left. We then plot typical periodic orbits through orbit classification, finding that the non-minimal coupling effect suppresses the orbital contraction induced by the magnetic charge, leading to degeneracy of orbits with different $$Q$$ values towards the Schwarzschild case, as well as phase shifts, amplitude enhancement, and period shortening in the gravitational waveforms with increasing $$Q$$ and $$\xi $$ . These results provide theoretical predictions for distinguishing different BH models through future gravitational wave observations.

Xiuqin He

Zhaoyi Xu

Meirong Tang

Non-minimally coupled Einstein–Yang–Mills black holes: periodic orbits and gravitational wave radiation in extreme mass ratio systems

An <italic>SO</italic>(3)-gauged Higgs model on IR 3 is proposed that, like the Abelian Higgs model on IR 2, features both attractive and repulsive phases, though unlike the latter its solutions do not saturate the topological lower bound. What distinguishes this model is that its energy is stabilised by the &#8220;Higgs analogue of the Chern-Pontryagin&#8221; charge, rather than the usual &#8220;Higgs&#8211;Chern-Pontryagin&#8221; charge which is a dimensional descendant of the Chern-Pontryagin charge.

Spain

Francisco Navarro-Lérida

Portugal

Eugen Radu

Ireland

D.H. Tchrakian

Attractive and repulsive Yang-Mills–Higgs magnetic monopoles on IR 3

We study the spin chain model which captures the one-loop spectral problem of a prototypical example of an <math altimg='si16.svg'><mrow><mi mathvariant='script'>N</mi><mo linebreak='goodbreak'>=</mo><mn>2</mn></mrow></math> SCFT in four dimensions. Up to date, this spin chain model remains unfathomable; the standard coordinate Bethe Ansatz does not lead to a solution from three magnons on, as the Yang-Baxter equation is not satisfied by the two-magnon scattering coefficients. In this paper, we find a long-range solution to the eigenvalue problem for three magnons. Remarkably, the scattering coefficients of particular subclasses of our solution, together with the position-dependent corrections, obey an infinite tower of modified Yang-Baxter equations. Our method of solving the three-magnon problem is interesting in its own right and generalizes the standard coordinate Bethe Ansatz approach to cases where the permutation symmetry is broken.

Deniz N Bozkurt

Juan Miguel Nieto García

Elli Pomoni

Long-range to the rescue of Yang-Baxter

We give a physical interpretation for the analytic continuation of the partition function of superconformal SU(2) 𝒩 = 2 gauge theory on the four-sphere to all values of the Yang-Mills coupling. We show that a well-motivated 2d construction associates two-dimensional unstable instantons to the 4d complex saddles which appear as singularities in the integrand of the supersymmetric localization expression. The construction is based on the chiral algebra subsector, and aligns with the alternative Higgs branch localization.

United Kingdom

Inês Aniceto

James Ratcliffe

Itamar Yaakov

The resurgence of errors in the localization of 𝒩 = 2 superconformal Yang-Mills

The space-time geometry under investigation is chosen to be a high-dimensional, static, spherically symmetric solution in an asymptotically flat background within the Einstein–power–Yang–Mills–Gauss–Bonnet (EPYMGB) gravity. To address the limitations of previous shadow constraints, we construct a standardized framework based on the Schwarzschild-Tangherlini metric to constrain the characteristic parameters. Additionally, we provide a rigorous derivation of the shadow radius formula for a general high-dimensional spherically symmetric black hole. Subsequently, we systematically and comprehensively present the effective potential equations governing spin-0, spin-1, $\textit{p}$-form, and spin-2 perturbations in high-dimensional static spherically symmetric flat space-time. Our analysis reveals that the Yang–Mills magnetic charge $$\mathcal {Q}$$ and the power $\textit{q}$ have a negligible impact on both the shadow radius and perturbations of the black hole when compared to the Gauss–Bonnet coupling constant $${\alpha }_2$$ in various dimensions. Hence, the physical signatures of the parameters $$\mathcal {Q}$$ and $\textit{q}$ in the black hole environment remain undetectable through either perturbation analysis or shadow observations. Cross-validation of the allowable range of $${\alpha }_2$$ derived from the high-dimensional constraint on shadow radius and the dynamical stability analysis of gravitational perturbations demonstrates excellent agreement between these independent approaches. The conclusions derived from the cross-analysis further substantiate the validity of the high-dimensional shadow constraint formula proposed in this work and indicate that the duality between black hole shadows and perturbations may persist in high-dimensional space-times.

Zening Yan

Constraints on shadow radius and instabilities arising from various perturbations in spherically symmetric black holes in Einstein–power–Yang–Mills–Gauss–Bonnet gravity