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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...

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 \( \mathcal{N} \) = 1 superconformal index for class \( \mathcal{S} \) fixed points

Christopher Beem 1 Abhijit Gadde 0 0 California Institute of Technology , Pasadena, CA 91125, U.S.A 1 Simons Center for Geometry and Physics, State University of New York , Stony Brook, NY 11794

Holomorphic blocks in three dimensions

We decompose sphere partition functions and indices of three-dimensional \( \mathcal{N} \) = 2 gauge theories into a sum of products involving a universal set of “holomorphic blocks”. The blocks count BPS states and are in one-to-one correspondence with the theory’s massive vacua. We also propose a new, effective technique for calculating the holomorphic blocks, inspired by a...

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...

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...

Cough and reflux esophagitis in children: their co-existence and airway cellularity

Background There are no prospective studies that have examined for chronic cough in children without lung disease but with gastroesophageal reflux (GER). In otherwise healthy children undergoing flexible upper gastrointestinal endoscopy (esophago-gastroscopy), the aims of the study were to (1) define the frequency of cough in relation to symptoms of GER, (2) examine if children...