Abstract
Four-dimensional 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 S. The class S duality web implies nontrivial associativity properties for the corresponding chiral algebras, the structure of which is best summarized in the language of generalized topological quantum field theory. We make a number of conjectures regarding the chiral algebras associated to various strongly coupled fixed points.
Highlights
A large and interesting class of interacting quantum field theories are the theories of class S [1, 2]
This structure follows from the defining property of theories of class S: they can be realized as the low energy limits of compactifications of six-dimensional CFTs with (2, 0) supersymmetry on punctured Riemann surfaces
We demonstrate that the reduction in the rank of a puncture is accomplished in the chiral algebra by quantum Drinfeld-Sokolov reduction, with the chiral algebra procedure mirroring the corresponding four-dimensional procedure involving a particular Higgsing of flavor symmetries
Summary
A large and interesting class of interacting quantum field theories are the theories of class S [1, 2]. An alternative — and perhaps more modern — tactic is to try to constrain or solve for various aspects of these theories using consistency conditions that follow from duality This approach was successfully carried out in [5] (building on the work of [6,7,8,9]) to compute the superconformal index of a very general set of class S fixed points (see [10, 11] for extensions to even more general cases). For a general strongly interacting SCFT, there is at present no straightforward method for identifying the associated chiral algebra Success in this task would implicitly fix an infinite amount of protected CFT data (spectral data and three-point couplings) that is generally difficult to determine. These methods are instrumental to the analysis of section 4
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