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Vertex operator algebras, Higgs branches, and modular differential equations

Abstract Every four-dimensional \( \mathcal{N}=2 \) superconformal field theory comes equipped with an intricate algebraic invariant, the associated vertex operator algebra. The relationships between this invariant and more conventional protected quantities in the same theories have yet to be completely understood. In this work, we aim to characterize the connection between the...

The Mellin formalism for boundary CFT d

We extend the Mellin representation of conformal field theory (CFT) to allow for conformal boundaries and interfaces. We consider the simplest holographic setup dual to an interface CFT — a brane filling an AdS d subspace of AdS d+1 — and perform a systematic study of Witten diagrams in this setup. As a byproduct of our analysis, we show that geodesic Witten diagrams in this...

Deformation Quantization and Superconformal Symmetry in Three Dimensions

We investigate the structure of certain protected operator algebras that arise in three-dimensional \({\mathcal{N}=4}\) superconformal field theories. We find that these algebras can be understood as a quantization of (either of) the half-BPS chiral ring(s). An important feature of this quantization is that it has a preferred basis in which the structure constants of the quantum...

The \( \mathcal{N}=2 \) superconformal bootstrap

In this work we initiate the conformal bootstrap program for \( \mathcal{N}=2 \) super-conformal field theories in four dimensions. We promote an abstract operator-algebraic viewpoint in order to unify the description of Lagrangian and non-Lagrangian theories, and formulate various conjectures concerning the landscape of theories. We analyze in detail the four-point functions of...

\( \mathcal{W} \) symmetry in six dimensions

Six-dimensional conformal field theories with (2, 0) supersymmetry are shown to possess a protected sector of operators and observables that are isomorphic to a two-dimensional chiral algebra. We argue that the chiral algebra associated to a (2, 0) theory labelled by the simply-laced Lie algebra \( \mathfrak{g} \) is precisely the \( \mathcal{W} \) algebra of type \( \mathfrak{g...

Chiral algebras of class \( \mathcal{S} \)

Four-dimensional \( \mathcal{N} \) = 2 superconformal field theories have families of protected correlation functions that possess the structure of two-dimensional chiral algebras. In this paper, we explore the chiral algebras that arise in this manner in the context of theories of class \( \mathcal{S} \). The class \( \mathcal{S} \) duality web implies nontrivial associativity...

The superconformal index of class \( \mathcal{S} \) theories of type D

Madalena Lemos 0 Wolfger Peelaers 0 Leonardo Rastelli 0 0 C.N. Yang Institute for Theoretical Physics, Stony Brook University , Stony Brook, NY 11794-3840, U.S.A We consider the superconformal

Resummation and S-duality in N = 4 SYM

We consider the problem of resumming the perturbative expansions for anomalous dimensions of low twist, non-BPS operators in four dimensional \( \mathcal{N} \) = 4 supersymmetric Yang-Mills theories. The requirement of S-duality invariance imposes considerable restrictions on any such resummation. We introduce several prescriptions that produce interpolating functions on the...