Publications

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Generalized symmetries of non-SUSY and discrete torsion string backgrounds

Noah Braeger, Vivek Chakrabhavi, Jonathan J. Heckman, Max Hübner

SciPost Phys. 19, 160 (2025) · published 18 December 2025 | · pdf

String / M-theory backgrounds with degrees of freedom at a localized singularity provide a general template for generating strongly correlated systems decoupled from lower-dimensional gravity. There are by now several complementary procedures for extracting the associated generalized symmetry data from orbifolds of the form $\mathbb{R}^6 / \Gamma$, including methods based on the boundary topology of the asymptotic geometry, as well as the adjacency matrix for fermionic degrees of freedom in the quiver gauge theory of probe branes. In this paper we show that this match between the two methods also works in non-supersymmetric and discrete torsion backgrounds. In particular, a refinement of geometric boundary data based on Chen-Ruan cohomology matches the expected answer based on quiver data. Additionally, we also show that free (i.e., non-torsion) factors count the number of higher-dimensional branes which couple to the localized singularity. We use this to also extract quadratic pairing terms in the associated symmetry theory (SymTh) for these systems, and explain how these considerations generalize to a broader class of backgrounds.
Instanton density operator in lattice QCD from higher category theory

Jing-Yuan Chen

SciPost Phys. 19, 158 (2025) · published 17 December 2025 | · pdf

A natural definition for instanton density operator in lattice QCD has long been desired. We show this problem is, and has to be, solved by higher category theory. The problem is solved by refining at a conceptual level the Yang-Mills theory on lattice, in order to recover the homotopy information in the continuum, which would have been lost if we put the theory on lattice in the traditional way. The refinement needed is a generalization—through the lens of higher category theory—of the familiar process of Villainization that captures winding in lattice XY model and Dirac quantization in lattice Maxwell theory. The apparent difference is that Villainization is in the end described by principal bundles, hence familiar, but more general topological operators can only be captured on the lattice by more flexible structures beyond the usual group theory and fibre bundles, making the language of categories natural and necessary. The key structure we need for our particular problem is called multiplicative bundle gerbe, based upon which we can construct suitable structures to naturally define the 2d Wess-Zumino-Witten term, 3d skyrmion density operator and 4d hedgehog defect for lattice $S^3$ (pion vacua) non-linear sigma model, and the 3d Chern-Simons term, 4d instanton density operator and 5d Yang monopole defect for lattice $SU(N)$ Yang-Mills theory; moreover, the structures behind the non-linear sigma model and the Yang-Mills theory are related via an implicit Yang-Baxter equation. In a broader perspective, higher category theory enables us to rethink more systematically the relation between continuum quantum field theory and lattice quantum field theory. We sketch a proposal towards a general machinery that constructs the suitably refined lattice degrees of freedom for a given non-linear sigma model or gauge theory in the continuum, realizing the desired topological operators on the lattice.
Dualities between 2+1d fusion surface models from braided fusion categories

Luisa Eck

SciPost Phys. 19, 157 (2025) · published 17 December 2025 | · pdf

Fusion surface models generalize the concept of anyon chains to 2+1 dimensions, utilizing fusion 2-categories as their input. We investigate bond-algebraic dualities in these systems and show that distinct module tensor categories $\mathcal{M}$ over the same braided fusion category $\mathcal{B}$ give rise to dual lattice models. This extends the 1+1d result that dualities in anyon chains are classified by module categories over fusion categories. We analyze two concrete examples: (i) a $\text{Rep}(S_3)$ model with a constrained Hilbert space, dual to the spin-$\tfrac{1}{2}$ XXZ model on the honeycomb lattice, and (ii) a bilayer Kitaev honeycomb model, dual to a spin-$\tfrac{1}{2}$ model with XXZ and Ising interactions. Unlike regular $\mathcal{M}=\mathcal{B}$ fusion surface models, which conserve only 1-form symmetries, models constructed from $\mathcal{M} ≠ \mathcal{B}$ can exhibit both 1-form and 0-form symmetries, including non-invertible ones.
Von Neumann subfactors and non-invertible symmetries

Xingyang Yu, Hao Y. Zhang

SciPost Phys. 19, 154 (2025) · published 15 December 2025 | · pdf

We use the language of von Neumann subfactors to investigate non-invertible symmetries in two dimensions. A fusion categorical symmetry $\mathcal{C}$, its module category $\mathcal{M}$, and a gauging labeled by an algebra object $\mathcal{A}$ are encoded in the bipartite principal graph of a subfactor. The dual principal graph captures the quantum symmetry $\mathcal{C}'$ obtained by gauging $\mathcal{A}$ in $\mathcal{C}$, as well as a reverse gauging back to $\mathcal{C}$. From a given subfactor $N \subset M$, we derive a quiver diagram that encodes the representations of the associated non-invertible symmetry. We show how this framework provides necessary conditions for admissible gaugings, enabling the construction of generalized orbifold groupoids. To illustrate this strategy, we present three examples: Rep$(D_4)$ as a warm-up, the higher-multiplicity case Rep$(A_4)$ with its associated generalized orbifold groupoid and triality symmetry, and Rep$(A_5)$, where $A_5$ is the smallest non-solvable finite group. For applications to gapless systems, we embed these generalized gaugings as global manipulations on the conformal manifolds of $c=1$ CFTs and uncover new self-dualities in the exceptional $SU(2)_1/A_5$ theory. For $\mathcal{C}$-symmetric TQFTs, we use the subfactor-derived quiver diagrams to characterize gapped phases, describe their vacuum structure, and classify the recently proposed particle-soliton degeneracies.
All fractional Shapiro steps in the RSJ model with two Josephson harmonics

Pavel N. Tsarev, Yakov V. Fominov

SciPost Phys. 19, 148 (2025) · published 8 December 2025 | · pdf

Synchronization between the internal dynamics of the superconducting phase in a Josephson junction (JJ) and an external ac signal is a fundamental physical phenomenon, manifesting as constant-voltage Shapiro steps in the current-voltage characteristic. Mathematically, this phase-locking effect is captured by the Resistively Shunted Junction (RSJ) model, an important example of a nonlinear dynamical system. The standard RSJ model considers an overdamped JJ with a sinusoidal (single-harmonic) current-phase relation (CPR) in the current-driven regime with a monochromatic ac component. While this model predicts only integer Shapiro steps, the inclusion of higher Josephson harmonics is known to generate fractional Shapiro steps. In this paper, we show that only two Josephson harmonics in the CPR are sufficient to produce all possible fractional Shapiro steps within the RSJ framework. Using perturbative methods, we analyze the amplitudes of these fractional steps. Furthermore, by introducing a phase shift between the two Josephson harmonics, we reveal an asymmetry between positive and negative fractional steps—a signature of the Josephson diode effect.
A family of vertex algebras from Argyres-Douglas theory

Heeyeon Kim, Jaewon Song

SciPost Phys. 19, 144 (2025) · published 2 December 2025 | · pdf

We find that multiple vertex algebras can arise from a single 4d $\mathcal{N}=2$ superconformal field theory (SCFT). The connection is given by the BPS monodromy operator $M$, which is a wall-crossing invariant quantity that captures the BPS spectrum on the Coulomb branch. For a class of low-rank Argyres-Douglas theories, we find that the trace of the multiple powers of the monodromy operator Tr$M^N$ yield modular functions that can be identified with the vacuum characters of certain vertex algebra for each $N$. In particular, we realize unitary VOAs of the Deligne-Cvitanović exceptional series type $(A_2)_1$, $(G_2)_1$, $(D_4)_1$, $(F_4)_1$, $(E_6)_1$ from Argyres-Douglas theories. We also find the modular invariant characters of the 'intermediate vertex algebras' $(E_{7\frac{1}{2}})_1$ and $(X_1)_1$. Our analysis allows us to construct 3d $\mathcal{N}=2$ gauge theories that flow to $\mathcal{N}=4$ SCFTs in the IR, whose specialized half-index can be identified with these modular invariant characters.
Exact solution for two $\delta$-interacting bosons on a ring in the presence of a $\delta$-barrier: Asymmetric Bethe Ansatz for spatially odd states

Maxim Olshanii, Mathias Albert, Gianni Aupetit-Diallo, Patrizia Vignolo, Steven G. Jackson

SciPost Phys. Core 8, 083 (2025) · published 12 November 2025 | · pdf

In this article, we apply the recently proposed Asymmetric Bethe Ansatz method to the problem of two one-dimensional, short-range-interacting bosons on a ring in the presence of a $\delta$-function barrier. Only half of the Hilbert space—namely, the two-body states that are odd under point inversion about the position of the barrier—is accessible to this method. The other half is presumably non-integrable. We consider benchmarking the recently proposed $1/g$ expansion about the hard-core boson point [D. Sen, Int. J. Mod. Phys. A 14, 1789 (1999); A. G. Volosniev et al., Nat. Commun. 5, 5300 (2014)] as one application of our results. Additionally, we find that when the $\delta$-barrier is converted to a $\delta$-well with strength equal to that of the particle-particle interaction, the system exhibits the spectrum of its non-interacting counterpart while its eigenstates display features of a strongly interacting system. We discuss this phenomenon in the "Summary and Future Research" section of our paper.
Bootstrapping nonequilibrium stochastic processes

Minjae Cho

SciPost Phys. 19, 124 (2025) · published 10 November 2025 | · pdf

We show that bootstrap methods based on the positivity of probability measures provide a systematic framework for studying both synchronous and asynchronous nonequilibrium stochastic processes on infinite lattices. First, we formulate linear programming problems that use positivity and invariance property of invariant measures to derive rigorous bounds on their expectation values. Second, for time evolution in asynchronous processes, we exploit the master equation along with positivity and initial conditions to construct linear and semidefinite programming problems that yield bounds on expectation values at both short and late times. We illustrate both approaches using two canonical examples: the contact process in 1+1 and 2+1 dimensions, and the Domany-Kinzel model in both synchronous and asynchronous forms in 1+1 dimensions. Our bounds on invariant measures yield rigorous lower bounds on critical rates, while those on time evolutions provide two-sided bounds on the half-life of the infection density and the temporal correlation length in the subcritical phase.
Geometric expansion of fluctuations and average shadows

Clément Berthière, Benoit Estienne, Jean-Marie Stéphan, William Witczak-Krempa

SciPost Phys. 19, 122 (2025) · published 7 November 2025 | · pdf

Fluctuations of observables provide unique insights into the nature of physical systems, and their study stands as a cornerstone of both theoretical and experimental science. Generalized fluctuations, or cumulants, provide information beyond the mean and variance of an observable. In this paper, we develop a systematic method to determine the asymptotic behavior of cumulants of local observables as the region becomes large. Our analysis reveals that the expansion is closely tied to the geometric characteristics of the region and its boundary, with coefficients given by convex moments of the connected correlation function: the latter is integrated against intrinsic volumes of convex polytopes built from the coordinates, which can be interpreted as average shadows. A particular application of our method shows that, in two dimensions, the leading behavior of odd cumulants of conserved quantities is topological, specifically depending on the Euler characteristic of the region. We illustrate these results with the paradigmatic strongly-interacting system of two-dimensional quantum Hall state at filling fraction $1/2$, by performing Monte-Carlo calculations of the skewness (third cumulant) of particle number in the Laughlin state.
Rényi entropies for one-dimensional quantum systems with mixed boundary conditions

Benoit Estienne, Yacine Ikhlef, Andrei Rotaru

SciPost Phys. 19, 119 (2025) · published 6 November 2025 | · pdf

We present a general method for calculating Rényi entropies in the ground state of a one-dimensional critical system with mixed open boundaries, for an interval starting at one of its ends. Technically, we consider the case when the boundary operator implementing the change of boundary conditions is degenerate under the Virasoro algebra. By exploiting the null-vectors conditions, we derive the ordinary differential equations that govern the scaling functions associated to the entropies. In particular, we provide an explicit formula for the second Rényi entropy. Additionally, we identify and compute the leading finite-size corrections to compare our theoretical results with numerical data for the Ising and three-state Potts critical chains.

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