Papers & preprints.

We demonstrate how horizon symmetries of AdS black holes are realised in the hydrodynamic actions for the dynamics of the dual stress tensor. A recent approach for obtaining such actions involves a choice of horizon boundary conditions, and we show that diffeomorphisms that preserve these give rise to symmetries of the corresponding hydrodynamic action. We obtain explicit hydrodynamic actions for small amplitude perturbations of black holes in JT and AdS$_3$ gravity using this approach and demonstrate explicitly the existence of these symmetries. For a natural choice of boundary conditions, the resulting actions manifestly realise gauge symmetries previously proposed for effective theories of maximal chaos.

In this paper we consider some general aspects of Euclidean conformal field theories on curved spaces of dimension $D\ge 3$. We first look at the OPE of scalar primary fields on conformally flat spaces. Extending the results of [see references in the paper], we give a general construction of the descendants' contributions to the OPE in the scalar channel. We then discuss CFTs on non-conformally flat spaces in the ambient space formalism. We investigate the short-distance behaviour of three-point functions on such spaces using the general ansatz proposed by Parisini, Skenderis, and Withers [see references in the paper]. We find that some additional corrections need to be added to the ansatz to ensure the existence of a local covariant OPE.

Characters of rational conformal field theories solve modular linear differential equations labelled by their order and the Wronskian index $\ell$. Direct classification of admissible solutions by solving MLDEs becomes increasingly difficult at higher $\ell$-- where movable poles and accessory parameters appear. In this work we introduce differential operators that relate higher-$\ell$ solutions to lower-$\ell$ ones while preserving modular covariance and integrality of the \(q\)-series. In rank two, this generates all allowed Wronskian sectors from the Mathur--Mukhi--Sen equation. In rank three and higher, it reduces the construction of higher-$\ell$ quasi-characters to simpler equations with lower $\ell$. This gives an efficient new route for organising candidate RCFT characters, and more generally quasi-characters, across the Wronskian tower. As an application, we apply our construction to prove a previously conjectured property on the signs of $\ell=2$ quasi-characters in rank 2.

We give a prescription to compute a dissipative action describing the large-scale thermal stress tensor dynamics of a holographic quantum field theory dual to AdS$_4$ gravity, in the context of the Schwinger-Keldysh formalism. Our prescription is valid to quadratic order in perturbations about the thermal equilibrium state. The hydrodynamical degrees of freedom of this action are realised in gravity as relative diffeomorphisms between the black hole horizon and the two asymptotic boundaries of the Crossley-Glorioso-Liu contour. We explicitly compute the action to first order in derivatives, and confirm it correctly reproduces the known hydrodynamic Green's functions. Our prescription requires a choice of horizon boundary conditions for the metric. We study the horizon symmetries that preserve these, and their relation to conjectured hydrodynamic symmetries responsible for many-body quantum chaos.

We develop a defect-theoretic refinement of meromorphic 2d CFTs in which the ordinary torus partition function -- often just the vacuum character -- does not reveal how states organize under symmetry lines. Our central proposal is an equatorial projection framework: from a commutant decomposition into commuting rational chiral algebras with categories $\mathcal{C}$ and $\widetilde{\mathcal{C}}$, we encode genus-one couplings by a non-negative integer matrix $M$ pairing characters and satisfying modular intertwiner relations. Invertible topological defect lines act directly on this gluing data (Verlinde lines diagonally via $S$-matrix eigenvalues, and anyon-permuting lines by braided-autoequivalence permutations), making modular covariance of defect amplitudes automatic and sharply distinguishing insertions that yield genuine modular invariants from those defining consistent non-holomorphic interfaces. We further show that the replacement rules of [see references in the paper] arise as equatorial projections of defect actions, and we extend these constructions beyond two-character examples by systematically treating three-character commutant pairs in the $E_{8,1}$ theory. The unique $c=8$ meromorphic CFT $E_{8,1}$ serves as a universal testbed, producing new defect partition functions and clarifying the roles of $\mathrm{Pic}(\mathcal{C})$ and $\mathrm{Aut}^{\mathrm{br}}(\mathcal{C})$. Finally, we outline extensions to higher central charges (e.g. $c=32,40$), yielding modular-invariant non-meromorphic theories beyond the $c=24$ Schellekens landscape [see references in the paper] as defect/interface descendants of meromorphic parents.

Rational conformal field theories in 2d have partition functions built from holomorphic characters, whose classification can be addressed via the holomorphic modular bootstrap. This is facilitated by a special basis of ``quasi-characters'' that has been completely classified for rank-2. Suitably combining these to form admissible characters with non-negative integral coefficients $a_n$ depends crucially on the signs and growth of the quasi-character coefficients. We use Frobenius recursion relations for Modular Linear Differential Equations to estimate the growth with $c$ of these coefficients in the region $n\sim\frac{c}{12}$ that is inaccessible to Cardy asymptotics, and to prove rigorously that they have alternating signs that stabilise to a fixed sign at this order. This provides a practical path to obtain candidate RCFT partition functions at arbitrary Wronskian index.

A comprehensive symmetry resolution of the entanglement entropy (EE) in $(1+1)$-d rational conformal field theories (RCFT) with categorical non-invertible symmetries is presented. This amounts to symmetry resolving the entanglement with respect to the generalized twisted and anyonic charge sectors of the theory. The anyonic sectors label the irreducible representations of a modular fusion category defining the symmetry and can be understood through the $(2+1)$-d symmetry topological field theory (SymTFT) that encodes the symmetry features of the CFT. Using this, we define the corresponding generalized boundary dependent charged moments necessary for the symmetry resolution of the entanglement entropy, which is the main result of this work. Furthermore, contrary to the case of invertible symmetries, we observe the breakdown of entanglement equipartition between different charged sectors at the next-to-leading order in the ultraviolet cutoff.

Chiral magnetohydrodynamics is devoted to understanding the late-time and long-distance behavior of a system with an Adler-Bell-Jackiw anomaly at finite temperatures. The non-conservation of the axial charge is determined by the topological density $\vec{E} \cdot \vec{B}$; in a classical hydrodynamic description this decay rate can be suppressed by tuning the background magnetic field to zero. However it is in principle possible for thermal fluctuations of $\vec{E} \cdot \vec{B}$ to result in a non-conservation of the charge even at vanishing $B$-field; this would invalidate the classical hydrodynamic effective theory. We investigate this by computing the real-time susceptibility of the topological density at one-loop level in magnetohydrodynamic fluctuations, relating its low-frequency limit to the decay rate of the axial charge. We find that the frequency-dependence of this susceptibility is sufficiently soft as to leave the axial decay rate unaffected, validating the classical hydrodynamic description. We show that the susceptibility contains non-analytic frequency-dependence which is universally determined by hydrodynamic data. We comment briefly on possible connections to the recent formulation of the ABJ anomaly in terms of non-invertible symmetry.

We propose a symmetry resolution of entanglement for categorical non-invertible symmetries (CaT-SREE) in (1 + 1)-dimensional CFTs. The definition parallels that of group-like invertible symmetries, employing the concept of symmetric boundary states with respect to a categorical symmetry. Our examination extends to rational CFTs, where the behavior of CaT-SREE mirrors that of group-like invertible symmetries. We find that CaT-SREE can be defined if there is no obstruction to gauging the categorical symmetry, as happens in the case of group-like symmetries. We also provide instances of the breakdown of entanglement equipartition at the next-to-leading order in the cutoff expansion. Our findings shed light on how the interplay between conformal boundary conditions and categorical symmetries lead to specific patterns in the entanglement entropy.

In this short note, we present a simple and elementary proof that meromorphic conformal field theories (CFTs) have central charges of the form: $c=8N$ with $N\in\mathbb{N}$ (the set of natural numbers) using the modular linear differential equations (MLDEs) approach. We first set up the 1-character MLDE for arbitrary value of the Wronskian index: $\ell$. From this we get the general form of the meromorphic CFT's character. We then study its modular transformations and the asymptotic value of it's Fourier coefficients -- using Rademacher series -- to conclude that odd values of $\ell$ make the character in-admissible implying that the central charge for admissible character has to be a multiple of 8.

We study classical lattice simulations of theories of electrodynamics coupled to charged matter at finite temperature, interpreting them using the higher-form symmetry formulation of magnetohydrodynamics (MHD). We compute transport coefficients using classical Kubo formulas on the lattice and show that the properties of the simulated plasma are in complete agreement with the predictions from effective field theories. In particular, the higher-form formulation allows us to understand from hydrodynamic considerations the relaxation rate of axial charge in the chiral plasma observed in previous simulations. A key point is that the resistivity of the plasma -- defined in terms of Kubo formulas for the electric field in the 1-form formulation of MHD -- remains a well-defined and predictive quantity at strong electromagnetic coupling. However, the Kubo formulas used to define the conventional conductivity vanish at low frequencies due to electrodynamic fluctuations, and thus the concept of the conductivity of a gauged electric current must be interpreted with care.

Studies of modular linear differential equations (MLDE) for the classification of rational CFT characters have been limited to the case where the coefficient functions (in monic form) have no poles, or poles at special points of moduli space. Here we initiate an exploration of the vast territory of MLDEs with two characters and any number of poles at arbitrary points of moduli space. We show how to parametrise the most general equation precisely and count its parameters. Eliminating logarithmic singularities at all the poles provides constraint equations for the accessory parameters. By taking suitable limits, we find recursion relations between solutions for different numbers of poles. The cases of one and two movable poles are examined in detail and compared with predictions based on quasi-characters to find complete agreement. We also comment on the limit of coincident poles. Finally we show that there exist genuine CFT corresponding to many of the newly-studied cases. We emphasise that the modular data is an output, rather than an input, of our approach.

We consider chiral magnetohydrodynamics, i.e. a finite-temperature system where an axial $U(1)$ current is not conserved due to an Adler-Bell-Jackiw anomaly saturated by the dynamical operator $F_{\mu\nu} \tilde{F}^{\mu\nu}$. We express this anomaly in terms of the 1-form symmetry associated with magnetic flux conservation and study its realization at finite temperature. We present Euclidean generating functional and dissipative action approaches to the dynamics and reproduce some aspects of chiral MHD phenomenology from an effective theory viewpoint, including the chiral separation and magnetic effects. We also discuss the construction of non-invertible axial symmetry defect operators in our formalism.

We investigate the admissible vector-valued modular forms having three independent characters and vanishing Wronskian index and determine which ones correspond to genuine 2d conformal field theories. This is done by finding bilinear coset-type relations that pair them into meromorphic characters with central charges 8, 16, 24, 32 and 40. Such pairings allow us to identify some characters with definite CFTs and rule out others. As a key result we classify all unitary three-character CFT with vanishing Wronskian index, excluding $c=8,16$. The complete list has two infinite affine series $B_{r,1},D_{r,1}$ and 45 additional theories. As a by-product, at higher values of the total central charge we also find constraints on the existence or otherwise of meromorphic theories. We separately list several cases that potentially correspond to Intermediate Vertex Operator Algebras.

In this work we extend the study of arXiv:2210.07186 by investigating two- and three-character MLDEs for Fricke groups at prime levels. We have constructed these higher-character MLDEs by using a $\mathit{novel}$ Serre-Ramanujan type derivative operator which maps $k$-forms to $(k+2)$-forms in $\Gamma^{+}_0(p)$. We found that this $\mathit{novel}$ derivative construction enabled us to write down a general prescription for obtaining $\mathit{Ramanujan-Eisenstein}$ identities for these groups. We discovered several $\mathit{novel}$ single-, two-, and three-character admissible solutions for Fricke groups at levels $2$ and $3$ after solving the MLDEs among which we have realized some in terms of Mckay-Thompson series and others in terms of modular forms of the corresponding Hecke groups. Among these solutions, we have identified interesting non-trivial bilinear identities. Furthermore, we could construct $\mathit{putative}$ partition functions for these theories based on these bilinear pairings, which could have a range of lattice interpretations. We also present and discuss modular re-parameterization of MLDE and their solutions for Fricke groups of prime levels.

In recent years it has been understood that new rational CFTs can be discovered by applying the coset construction to meromorphic CFTs. Here we turn this approach around and show that the coset construction, together with the classification of meromorphic CFT with $c\leq 24$, can be used to predict the existence of new meromorphic CFTs with $c\geq 32$ whose Kac-Moody algebras are non-simply-laced and/or at levels greater than 1. This implies they are non-lattice theories. Using three-character coset relations, we propose 34 infinite series of meromorphic theories with arbitrarily large central charge, as well as 46 theories at $c=32$ and $c=40$.

In $U(1)$ Abelian gauge theory coupled to fermions, the non-conservation of the axial current due to the chiral anomaly is given by a dynamical operator $F_{\mu\nu} \tilde{F}^{\mu\nu}$ constructed from the field-strength tensor. We attempt to describe this physics in a universal manner by casting this operator in terms of the 2-form current for the 1-form symmetry associated with magnetic flux conservation. We construct a holographic dual with this symmetry breaking pattern and study some aspects of finite temperature anomalous magnetohydrodynamics. We explicitly calculate the charge susceptibility and the axial charge relaxation rate as a function of temperature and magnetic field and compare to recent lattice results. At small magnetic fields we find agreement with elementary hydrodynamics weakly coupled to an electrodynamic sector, but we find deviations at larger fields.

In the modular linear differential equation (MLDE) approach to classifying rational conformal field theories (RCFTs) both the MLDE and the RCFT are identified by a pair of non-negative integers $\textbf{[n,l]}$. $\mathbf{n}$ is the number of characters of the RCFT as well as the order of the MLDE that the characters solve and $\mathbf{l}$, the Wronskian index, is associated to the structure of the zeroes of the Wronskian of the characters. In this paper, we study $\textbf{[3,0]}$ and $\textbf{[3,2]}$ MLDEs in order to classify the corresponding CFTs. We reduce the problem to a "finite" problem: to classify CFTs with central charge $ 0 < c \leq 96$, we need to perform $6,720$ computations for the former and $20,160$ for the latter. Each computation involves (i) first finding a simultaneous solution to a pair of Diophantine equations and (ii) computing Fourier coefficients to a high order and checking for positivity. In the $\textbf{[3,0]}$ case, for $ 0 < c \leq 96$, we obtain many character-like solutions: two infinite classes and a discrete set of $303$. After accounting for various categories of known solutions, including Virasoro minimal models, WZW CFTs, Franc-Mason vertex operator algebras and Gaberdiel-Hampapura-Mukhi novel coset CFTs, we seem to have seven hitherto unknown character-like solutions which could potentially give new CFTs. We also classify $\textbf{[3,2]}$ CFTs for $ 0 < c \leq 96$: each CFT in this case is obtained by adjoining a constant character to a $\textbf{[2,0]}$ CFT, whose classification was achieved by Mathur-Mukhi-Sen three decades ago.

The classification scheme for rational conformal field theories, given by the Mathur-Mukhi-Sen (MMS) program, identifies a rational conformal field theory by two numbers: $(n, l)$. $n$ is the number of characters of the rational conformal field theory. The characters form linearly independent solutions to a modular linear differential equation (which is also labelled by $(n, l)$); the Wronskian index $l$ is a non-negative integer associated to the structure of zeroes of the Wronskian. In this paper, we compute the $(n, l)$ values for three classes of well-known CFTs viz. the WZW CFTs, the Virasoro minimal models and the $\mathcal{N} = 1$ super-Virasoro minimal models. For the latter two, we obtain exact formulae for the Wronskian indices. For WZW CFTs, we get exact formulae for small ranks (upto 2) and all levels and for all ranks and small levels (upto 2) and for the rest we compute using a computer program. We find that any WZW CFT at level 1 has a vanishing Wronskian index as does the $\mathbf{\hat{A}_1}$ CFT at all levels. We find intriguing coincidences such as: (i) for the same level CFTs with $\mathbf{\hat{A}_2}$ and $\mathbf{\hat{G}_2}$ have the same $(n,l)$ values, (ii) for the same level CFTs with $\mathbf{\hat{B}_r}$ and $\mathbf{\hat{D}_r}$ have the same $(n,l)$ values for all $r \geq 5$. Classifying all rational conformal field theories for a given $(n, l)$ is one of the aims of the MMS program. We can use our computations to provide partial classifications. For the famous $(2, 0)$ case, our partial classification turns out to be the full classification (achieved by MMS three decades ago). For the $(3, 0)$ case, our partial classification includes two infinite series of CFTs as well as seven ``discrete'' CFTs; except two all others have Kac-Moody symmetry.

Black hole radiation from an infinitesimally thin massive collapsing shell, possessing a global monopole charge, which in turn leads to a Schwarzschild black hole with a global monopole charge has been shown to be processed by a unitary evolution. The exterior metric of the collapsing shell is described by the global monopole (GM) metric. The analysis is performed using the Wheeler-deWitt formalism which gave rise to a Schrödinger-like wave equation. Existence of unitarity is confirmed from two independent lines of approach. Firstly, by showing that the trace of the square of the density matrix, of the outgoing radiation, from a quantized massless scalar field, is unity. Secondly, by proving that the conservation of probability holds for the wave function of the system.

We have shown analytically that radiation from a collapsing shell which leads to a charged black hole, whose exterior is described by the RN (Reissner-Nordström) metric (and hence the background spacetime is non-globally hyperbolic), is processed with a unitary evolution. For the analysis, we have used the Wheeler-deWitt formalism which in turn gave rise to a Schrödinger-like wave equation. We showed the existence of unitarity by proving that the trace of the squared density matrix of the outgoing radiation, from a quantized massless scalar field, is unity and that the conservation of probability holds for the wave function of the system.