We further investigate the 3d gauged linear sigma model (GLSM)/ quantum K-theory correspondence for partial flag manifolds $\textit{X}$ ≡ Fl( ; $\textit{n}$). This is a 3d uplift of the 2d GLSM/quantum cohomology correspondence with the 3d theory compactified on $$ {\mathbb{R}}^2\times {S}_{\beta}^1 $$ . Recently, a set of half-BPS line operators, called Schubert line defects, were constructed that correspond to the Schubert classes in the K-theory ring of $\textit{X}$. Utilizing algebro-geometric algorithms, we compute 2-point and 3-point correlation functions of these line operators in the 3d A-model regime of the theory. These are interpreted as genus-0 K-theoretic Gromov-Witten invariants, and they produce the K-theoretic Littlewood-Richardson coefficients of the quantum K-theory ring of $\textit{X}$. We show how this works explicitly in examples, going beyond the existing results in the literature. Taking the small $\textit{β}$ limit, we apply these techniques to the resulting 2d GLSM. We explicitly compute the quantum cohomology ring relations of $\textit{X}$ for some cases and match with existing results in the literature in examples.

Switzerland

Zhihao Duan

France

Osama Khlaif

China

Hao Zou

On the Schubert calculus of the quantum K-theory for partial flag manifolds: a 3d A-model perspective

We investigate thermal photon production in the quark-gluon plasma (QGP) under strong magnetic fields using a magnetohydrodynamic (MHD) framework. We employ relativistic ideal fluid dynamics under the non-resistive approximation by adopting the Bjorken flow model with power-law decaying magnetic fields $ \mathbf{B}(\tau) = \mathbf{B}_0 (\tau_0/\tau)^a $ , span> $\textit{a}$ controls the decay rate, $ B_0 = \sqrt{\sigma} T_0^2 $ , and $\textit{σ}$ characterizes the initial field strength. The resulting QGP temperature evolution exhibits distinct $\textit{a}$- and $\textit{σ}$-dependent behaviors. Thermal photon production rates are calculated for three dominant processes: Compton scattering with $ q\bar{q} $ annihilation (C+A), bremsstrahlung (Brems), and $ q\bar{q} $ annihilation with additional scattering (A+S). These rates are integrated over the space-time volume to obtain the photon transverse momentum $ (p_T) $ spectrum. Our results demonstrate that increasing $\textit{a}$ enhances photon yields across all $ p_T $ , with $ a \to \infty $ (super-fast decay) providing an upper bound. For $ a = 2/3 $ , a larger $\textit{σ}$ suppresses yields through accelerated cooling, whereas for $ a \to \infty $ , a larger $\textit{σ}$ enhances yields via prolonged thermal emission. Low- $ p_T $ photons receive significant contributions from all QGP evolution stages, while high- $ p_T $ photons originate predominantly from early times. The central rapidity region $ (y=0) $ dominates the total yield. This work extends the photon yield studies to the MHD regime under strong magnetic fields, clarifying the magnetic field effects on QGP electromagnetic signatures and establishing foundations for future investigations of magnetization and dissipative phenomena.

Jie Xiong

Xiang Fan

Jing Jing

Weishan Yang

Duan She

Ze-Fang Jiang

Thermal photon emission from quark-gluon plasma: 1+1D magnetohydrodynamics results * Supported by the National Natural Science Foundation of China (NSFC) (12305138). Duan She's research is funded by the Startup Research Fund of Henan Academy of Sciences (231820058) and the 2024 Henan Province International Science and Technology Cooperation Projects (242102521068)

We study $\textit{ℤ}$ one-form center symmetries in four-dimensional gauge theories using the symmetry topological field theory (SymTFT). In this context, the associated TFT in the five-dimensional bulk is the BF model. We revisit its canonical quantization and construct topological boundary states on several important classes of four manifolds that are spin, non-spin and torsional. We highlight a web of four-dimensional dualities, which can be naturally interpreted within the SymTFT framework. We also point out an intriguing class of four-dimensional gauge theories that exhibit mixed ’t Hooft anomaly between one-form symmetries. In the second part of this work, we extend the SymTFT to account for various quantities protected by supersymmetry (SUSY) in SUSY gauge theories. We proposed that their behaviour under various symmetry operations are entirely captured by the topological boundary of the SymTFT, resulting in strong constraints. Concrete examples are considered, including the Witten index, the lens space index and the Donaldson-Witten and Vafa-Witten partition functions.

United Kingdom

South Korea

Qiang Jia

Sungjay Lee

Web of 4D dualities, supersymmetric partition functions and SymTFT

We study particular integrated correlation functions of two superconformal primary operators of the stress tensor multiplet in the presence of a half-BPS line defect labelled by electromagnetic charges ($\textit{p}$, $\textit{q}$) in $$ \mathcal{N} $$ = 4 supersymmetric Yang-Mills theory (SYM) with gauge group SU($\textit{N}$). An important consequence of SL(2, $\textit{ℤ}$) electromagnetic duality in $$ \mathcal{N} $$ = 4 SYM is that correlators of line defect operators with different charges ($\textit{p}$, $\textit{q}$) must be related in a non-trivial manner when the complex coupling $\textit{τ}$ = $\textit{θ}$/(2$\textit{π}$) + $$ 4\pi i/{g}_{\textrm{YM}}^2 $$ is transformed appropriately. In this work we introduce a novel class of real-analytic functions whose automorphic properties with respect to SL(2, $\textit{ℤ}$) match the expected transformations of line defect operators in $$ \mathcal{N} $$ = 4 SYM under electromagnetic duality. At large $\textit{N}$ and fixed $\textit{τ}$, the correlation functions we consider are related to scattering amplitudes of two gravitons from extended ($\textit{p}$, $\textit{q}$)-strings in the holographic dual type IIB superstring theory. We show that the large-$\textit{N}$ expansion coefficients of the integrated two-point line defect correlators are given by finite linear combinations with rational coefficients of elements belonging to this class of automorphic functions. On the other hand, for any fixed value of $\textit{N}$ we conjecture that the line defect integrated correlators can be expressed as formal infinite series over such automorphic functions. The resummation of this series produces a simple lattice sum representation for the integrated line defect correlator that manifests its automorphic properties. We explicitly demonstrate this construction for the cases with gauge group SU(2) and SU(3). Our results give direct access to non-perturbative integrated correlators in the presence of an ’t Hooft-line defect, observables otherwise very difficult to compute by other means.

Germany

Daniele Dorigoni

Italy

Daniele Pavarini

Congkao Wen

United States

Haitian Xie

Electromagnetic duality for line defect correlators in $$ \mathcal{N} $$ = 4 super Yang-Mills theory

Given a two-dimensional bosonic theory with a non-anomalous ℤ2 symmetry, the orbifolding and fermionization can be understood holographically using three-dimensional BF theory with level 2. From a Hamiltonian perspective, the information of dualities is encoded in a topological boundary state which is defined as an eigenstate of certain Wilson loop operators (anyons) in the bulk. We generalize this story to two-dimensional theories with non-anomalous ℤ N  symmetry, focusing on parafermionization. We find the generic operators defining different topological boundary states including orbifolding and parafermionization with ℤ N  or subgroups of ℤ N , and discuss their algebraic properties as well as the ℤ N  duality web.

ℤ N  duality and parafermions revisited

In this note we study the resurgent structure of sl(2, ℂ) Chern-Simons state integral model on knot complements S 3\4 1 , S 3\5 2 with generic discrete level k ≥ 1 and with small boundary holonomy deformation. The coefficients of the saddle point expansions are in the trace field of the knot extended by the holonomy parameter. Despite increasing complication of the asymptotic series as the level k increases, the resurgent structure of the asymptotic series is universal: both the distribution of Borel plane singularities and the associated Stokes constants are independent of the level k.

Jie Gu

Resurgence in complex Chern-Simons theory at generic levels

We utilize the integrality conjecture to show that the torus partition function of a fermionic rational conformal theory in the Ramond-Ramond sector becomes a constant when the bound <math><msup><mi>h</mi><mi>R</mi></msup><mo>≥</mo><mfrac><mi>c</mi><mn>24</mn></mfrac></math> is satisfied, where <math><msup><mi>h</mi><mi>R</mi></msup></math> denotes the conformal weights of Ramond states and <math><mi>c</mi></math> is the central charge. The constant-valued Ramond-Ramond partition function strongly suggests the presence of supersymmetry unless a given theory has free fermions. The lower bound <math><msup><mi>h</mi><mi>R</mi></msup><mo>≥</mo><mfrac><mi>c</mi><mn>24</mn></mfrac></math> can then be identified with the unitarity bound of <math><mi>N</mi><mo>=</mo><mn>1</mn></math> supersymmetry. We thus propose that, for rational CFTs without free fermions, <math><mo>(</mo><msup><mi>h</mi><mi>R</mi></msup><mo>−</mo><mi>c</mi><mo>/</mo><mn>24</mn><mo>)</mo><mo>≥</mo><mn>0</mn></math> can imply supersymmetry.

Jin-Beom Bae

Can the energy bound <math><mi>E</mi><mo>≥</mo><mn>0</mn></math> imply supersymmetry?

We systematically study how the integrality of the conformal characters shapes the space of fermionic rational conformal field theories in two dimensions. The integrality suggests that conformal characters on torus with a given choice of spin structures should be invariant under a principal congruence subgroup of PSL(2, ℤ). The invariance strongly constrains the possible values of the central charge as well as the conformal weights in both Neveu-Schwarz and Ramond sectors, which improves the conventional holomorphic modular bootstrap method in a significant manner. This allows us to make much progress on the classification of fermionic rational conformal field theories with the number of independent characters less than five.

Kimyeong Lee

Linfeng Li

On classification of fermionic rational conformal field theories

We systemically study the Hecke relations and the c = 8k coset relations among 2d rational conformal field theories (RCFTs) with up to seven characters. We propose that the characters of any 2d RCFT — unitary or non-unitary — satisfying a holomorphic modular linear differential equation (MLDE) can be realized as either a Hecke image or the coset of a Hecke image with respect to a c = 8k theory. Benefited from the recent results on holomorphic modular bootstrap, we check this proposal for all admissible theories with up to five characters. We also find many new interesting Hecke relations. For example, the characters of WZW models (E 6)2 , (E 7)2 , (  <math> <msub> <mi>E</mi> <mrow> <mn>7</mn> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </msub> </math>  $$ {E}_{7\frac{1}{2}} $$ )2 can be realized as the Hecke images T13 , T19 , T19 of Virasoro minimal models M sub(7, 6), M(5, 4), M eff(13, 2) respectively. Besides, we find the characters associated to the second largest Fisher group Fi 23 and the Harada-Norton group HN can be realized as the Hecke images T23 , T19 of the product theories M eff(5, 2) ⊗ M eff(7, 2) and M eff(7, 2)⊗2 respectively. Mathematically, our study provides a great many interesting examples of vector-valued modular functions up to rank seven.

Kaiwen Sun

Hecke relations, cosets and the classification of 2d RCFTs

Recently, the modular linear differential equation (MLDE) for level-two congruence subgroups Γ θ  , Γ0(2) and Γ0(2) of SL2(ℤ) was developed and used to classify the fermionic rational conformal field theories (RCFT). Two character solutions of the second-order fermionic MLDE without poles were found and their corresponding CFTs are identified. Here we extend this analysis to explore the landscape of three character fermionic RCFTs obtained from the third-order fermionic MLDE without poles. Especially, we focus on a class of the fermionic RCFTs whose Neveu-Schwarz sector vacuum character has no free-fermion currents and Ramond sector saturates the bound h R ≥   <math> <mfrac> <mi>C</mi> <mn>24</mn> </mfrac> </math>  $$ \frac{C}{24} $$ , which is the unitarity bound for the supersymmetric case. Most of the solutions can be mapped to characters of the fermionized WZW models. We find the pairs of fermionic CFTs whose characters can be combined to produce K(τ), the character of the c = 12 fermionic CFT for Co0 sporadic group.