We present integrable deformations of Yang-Baxter (YB) sigma models based on the Courant-Hilbert (CH) construction. To this end, we employ the four-dimensional Chern-Simons theory, in which the CH construction is shown in arXiv:2509.22080. As a result, the CH construction works in an intricate way alongside the YB deformations. Remarkably, the resulting deformed action can also be expressed as the sum of the master formula Lagrangian and the trace of the energy-momentum tensor. This result indicates the universality of the correction term.

Japan

Osamu Fukushima

Takaki Matsumoto

Kentaroh Yoshida

Courant-Hilbert deformations of Yang-Baxter sigma models

We compute solutions to the Hermitian Yang-Mills equations on holomorphic vector bundles $\textit{V}$ via an alternating optimisation procedure founded on geometric machine learning. The proposed method is fully general with respect to the rank and structure group of $\textit{V}$, requiring only the ability to enumerate a basis of global sections for a given bundle. This enables us to compute the physically normalised Yukawa couplings in a broad class of heterotic string compactifications. Using this method, we carry out this computation in full for a heterotic compactification incorporating a gauge bundle with non-Abelian structure group.

United Kingdom

Challenger Mishra

Justin Tan

Hermitian Yang-Mills connections on general vector bundles: geometry and physical Yukawa couplings

We study Wilson loops on the Coulomb branch of $\textit{N}$ = 4 super-Yang-Mills theory, by solving for minimal surface that connect the contour on the boundary with the D3-brane in the bulk. The circular loop undergoes the Gross-Ooguri transition as a function of the radius and angular separation, and we fully map its phase diagram. As a byproduct we find evidence that the expectation value of the straight line is tree-level exact.

Belgium

Jarne Moens

Denmark

Sweden

Konstantin Zarembo

Wilson loops on the Coulomb branch of N=4 super-Yang-Mills

We initiate the study of flux tubes in confining gauge theories placed in a rigid AdS background, which serves as an infrared regulator. Varying the AdS radius from large to small allows us to interpolate between the flat space confining string, and a weakly coupled string-like object which is held together by the AdS gravitational potential. At any radius, the string preserves a subgroup of AdS isometries equivalent to the one-dimensional conformal group and hence, from the boundary point of view, can be thought of as a conformal defect. The defect hosts a protected operator, called displacement, which nonlinearly realizes the broken AdS isometries. At small radius the displacement corresponds to the gauge field strength inserted at the boundary, while at large radius it is mapped to the Goldstone mode living on the string worldsheet. This relates gauge field and worldsheet degrees of freedom. We propose a hypothesis according to which the large and small radius perturbative expansions can be smoothly matched with each other. As a test, we calculate the leading order corrections to the scaling dimensions and OPE coefficients of a set of defect operators at weak coupling in planar 3D Yang-Mills.

Switzerland

Barak Gabai

Victor Gorbenko

Jiaxin Qiao

Yang-Mills flux tube in AdS

We discuss 4D N=2 non-abelian gauge theories where one supersymmetry is preserved while the other one is spontaneously broken and non-linearly realized. The goldstino resides in a Maxwell multiplet of the Bagger–Galperin type. We introduce appropriate constraints that eliminate the chiral N=1 superfield sector of the non-abelian N=2 multiplets and discuss the properties of the leading order Lagrangians.

Greece

Fotis Farakos

Ulf Lindström

Super Yang–Mills with partially non-linear extended supersymmetry

The multicritical generalizations of the Lee-Yang universality class arise as renormalization-group fixed points of scalar field theories with complex $\textit{iφ}$ interaction, $\textit{n}$ ∈ ℕ, just below their upper critical dimension. It has been recently conjectured that their continuation to two dimensions corresponds to the non-unitary conformal minimal models ℳ(2$\textit{,}$ 2$\textit{n}$ + 3). Motivated by that, we revisit the functional renormalization group approach to complex 𝒫𝒯-symmetric scalar field theories in the Local Potential Approximation, without or with wavefunction renormalization (LPA and LPA’ respectively), aiming to explore the fate of the $\textit{iφ}$ theories from their upper critical dimension to two dimensions. The $\textit{iφ}$ fixed points are identified using a perturbative expansion of the functional fixed-point equation near their upper critical dimensions, and they are followed to lower dimensions by numerical integration of the full equation. A peculiar feature of the complex 𝒫𝒯-symmetric potentials is that the fixed points are characterized by real but negative anomalous dimensions $\textit{η}$, and in low dimension $\textit{d}$, this can lead to a change of sign of the scaling dimensions ∆ = ($\textit{d}$ − 2 + $\textit{η}$)$\textit{/}$2, thus requiring a novel analysis of the analytical properties of the functional fixed-point equations. We are able to follow the Lee-Yang universality class ($\textit{n}$ = 1) down to two dimensions, and numerically determine the scaling dimension of the fundamental field as a function of $\textit{d}$. On the other hand, within the LPA’, multicritical Lee-Yang fixed points with $\textit{n >}$ 1 cannot be continued to $\textit{d}$ = 2 due to the existence of unexpected non-perturbative fixed points that annihilate with the $\textit{iφ}$ fixed points.

France

Dario Benedetti

Fanny Eustachon

Italy

Omar Zanusso

Critical and multicritical Lee-Yang fixed points in the local potential approximation

We analyze the behavior of holographic subregion complexity (HSC) and holographic fidelity susceptibility (HFS) in noncommutative Yang-Mills theory. The emergence of a minimum length scale, dictated by the degree of noncommutativity, induces a behavioral transition in the HSC and establishes a lower bound. In the large noncommutativity regime, the qualitative features of the complexity deviate significantly from the commutative case. The HFS is shown to provide an effective measure of the degree of noncommutativity. Although the HSC generally satisfies strong subadditivity, this property fails abruptly when the subregion size approaches the minimum length scale. At finite temperature, the long-range behavior of the HSC is modified, and its lower bound scales positively with temperature. Furthermore, temperature enhances the sensitivity of the fidelity susceptibility to the degree of noncommutativity. Within the AdS soliton background, a competition between connected and disconnected configurations arises in the HSC, signaling a phase-transition-like behavior. Finally, the compactification scale is found to diminish the sensitivity of the HFS to the degree of noncommutativity.

Tadahito Nakajima

Holographic subregion complexity and fidelity susceptibility in noncommutative Yang-Mills theory

We study $$ \mathcal{N} $$ = 4 super Yang-Mills theory compactified on an S at zero temperature, with VEVs for two scalar bilinears and three independent current sources. We show that type IIB supergravity provides a complete holographic description of this setup, admitting both supersymmetric and non-supersymmetric AdS-soliton solutions that are asymptotically AdS and smooth in the IR. The current sources correspond in 2+1 dimensions to Q-ball charge densities for U(1) ⊂ SO(6) , and are geometrically realized as twists along three angular directions of the S . We demonstrate that the bulk dynamics encodes the full vacuum structure of the dual field theory and explicitly reconstruct the supersymmetric moduli space.

Brazil

Chile

Andrés Anabalón

Horatiu Nastase

Carlos Nunez

Spain

Marcelo Oyarzo

Ricardo Stuardo

Moduli space of $$ \mathcal{N} $$ = 4 super Yang-Mills from AdS/CFT

We study the resurgent structure of the topological string dual to 2d U($\textit{N}$) Yang-Mills on torus. We find closed form formulas for instanton amplitudes up to arbitrarily high instanton orders, based on which we propose the non-perturbative partition function including contributions from all the real instantons, which is real for positive modulus and string coupling. We also explore complex instantons and find two infinite towers of them. We expect them to correspond to BPS states in type II string.

China

Jiashen Chen

Jie Gu

Xin Wang

Resurgent structure of 2d Yang-Mills theory on a torus

We consider planar $$ \mathcal{N} $$ = 4 super Yang-Mills at finite temperature with chemical potentials that couple either to the $\textit{R}$-charges or the spins of the operators. We find expressions for the Hagedorn temperatures at both zero coupling by explicitly counting states, and at strong coupling using the string theory dual. We then apply the quantum spectral curve (QSC) to this problem, which adds additional twists to the $\textit{Q}$-functions. For a single chemical potential $\textit{μ}$ coupled to one of the $\textit{R}$-charges, we find the analytic weak-coupling Hagedorn temperature to one-loop order for any value of $\textit{μ}$, and to two-loop order for $\textit{μ}$ = 1/2. We then solve the QSC numerically, showing that at strong coupling there is good agreement with the string theory prediction to order 1/$\textit{λ}$ . This provides further evidence for a recent conjecture of Harmark for the form of the world-sheet zero-point shift. We also use the QSC to find the analytic one-loop correction to the Hagedorn temperature with non-zero chemical potentials coupled to the spins.

Simon Ekhammar

United States

Joseph Minahan

Charles Thull

Twisting the Hagedorn temperature in planar $$ \mathcal{N} $$ = 4 super Yang-Mills