Symmetry-resolved entanglement for excited states and two entangling intervals in AdS3/CFT2

We test the proposal of [1] for the holographic computation of the charged moments and the resulting symmetry-resolved entanglement entropy in different excited states, as well as for two entangling intervals. Our holographic computations are performed in U(1) Chern-Simons-Einstein-Hilbert gravity, and are confirmed by independent results in a conformal field theory at large central charge. In particular, we consider two classes of excited states, corresponding to charged and uncharged conical defects in AdS3. In the conformal field theory, these states are generated by the insertion of charged and uncharged heavy operators. We employ the monodromy method to calculate the ensuing four-point function between the heavy operators and the twist fields. For the two-interval case, we derive our results on the AdS and the conformal field theory side, respectively, from the generating function method of [1], as well as the vertex operator algebra. In all cases considered, we find equipartition of entanglement between the different charge sectors. We also clarify an aspect of conformal field theories with a large central charge and $$ \hat{\mathfrak{u}}{(1)}_k $$ u ̂ 1 k Kac-Moody symmetry used in our calculations, namely the factorization of the Hilbert space into a gravitational Virasoro sector with large central charge, and a $$ \hat{\mathfrak{u}}{(1)}_k $$ u ̂ 1 k Kac-Moody sector.

The Quantum Group Dual of the First-Row Subcategory for the Generic Virasoro VOA

In several examples it has been observed that a module category of a vertex operator algebra (VOA) is equivalent to a category of representations of some quantum group. The present article is concerned with developing such a duality in the case of the Virasoro VOA at generic central charge; arguably the most rudimentary of all VOAs, yet structurally complicated. We do not address the category of all modules of the generic Virasoro VOA, but we consider the infinitely many modules from the first row of the Kac table. Building on an explicit quantum group method of Coulomb gas integrals, we give a new proof of the fusion rules, we prove the analyticity of compositions of intertwining operators, and we show that the conformal blocks are fully determined by the quantum group method. Crucially, we prove the associativity of the intertwining operators among the first-row modules, and find that the associativity is governed by the 6j-symbols of the quantum group. Our results constitute a concrete duality between a VOA and a quantum group, and they will serve as the key tools to establish the equivalence of the first-row subcategory of modules of the generic Virasoro VOA and the category of (type-1) finite-dimensional representations of $${\mathcal {U}}_q (\mathfrak {sl}_2)$$ U q ( sl 2 ) .

Foliation of a space associated to vertex operator algebra

In this paper, we construct the foliation of a space associated to correlation functions of vertex operator algebras, considered on Riemann surfaces. We prove that the computation of general genus g correlation functions determines a foliation on the space associated to these correlation functions a sewn Riemann surface. Certain further applications of the definition are proposed.

A domain wall in twisted M-theory

We study a four-dimensional domain wall in twisted M-theory. The domain wall is engineered by intersecting D6 branes in the type IIA frame. We identify the classical algebra of operators on the domain wall in terms of a higher vertex operator algebra, which describes the holomorphic subsector of a 4d \mathcal{N}=1𝒩=1 supersymmetric field theory, and compute the associated mode algebra. We conjecture that the quantum deformation of the classical algebra is isomorphic to the bulk algebra of operators from which we establish twisted holography of the domain wall.

Q-Systems and Extensions of Completely Unitary Vertex Operator Algebras

Complete unitarity is a natural condition on a CFT-type regular vertex operator algebra (VOA), which ensures that its modular tensor category (MTC) is unitary. In this paper we show that any CFT-type unitary (conformal) extension $U$ of a completely unitary VOA $V$ is completely unitary. Our method is to relate $U$ with a Q-system $A_U$ in the $C^*$-tensor category $\textrm{Rep}^{\textrm{u}}(V)$ of unitary $V$-modules. We also update the main result of [ 30] to the unitary cases by showing that the tensor category $\textrm{Rep}^{\textrm{u}}(U)$ of unitary $U$-modules is equivalent to the tensor category $\textrm{Rep}^{\textrm{u}}(A_U)$ of unitary $A_U$-modules as unitary MTCs. As an application, we obtain infinitely many new (regular and) completely unitary VOAs including all CFT-type $c<1$ unitary VOAs. We also show that the latter are in one-to-one correspondence with the (irreducible) conformal nets of the same central charge $c$, the classification of which is given by [ 29].

Permutation orbifolds of 𝔰𝔩2 vertex operator algebras

We analyze two types of permutation orbifolds: (i) S2-orbifolds of the universal level k vertex operator algebra Vk(𝔰𝔩2) and of its simple quotient Lk(𝔰𝔩2), and (ii) the S3-orbifold of the level one simple vertex operator algebra L1(𝔰𝔩2). We determine their structures and discuss related W-algebras.