Bootstrapping mathcal{N}=3 superconformal theories

Madalena Lemos,Vladimir Mitev,Carlo Meneghelli,Pedro Liendo

doi:10.1007/jhep04(2017)032

Abstract

We initiate the bootstrap program for mathcal{N}=3 superconformal field theories (SCFTs) in four dimensions. The problem is considered from two fronts: the protected subsector described by a 2d chiral algebra, and crossing symmetry for half-BPS operators whose superconformal primaries parametrize the Coulomb branch of mathcal{N}=3 theories. With the goal of describing a protected subsector of a family of mathcal{N}=3 SCFTs, we propose a new 2d chiral algebra with super Virasoro symmetry that depends on an arbitrary parameter, identified with the central charge of the theory. Turning to the crossing equations, we work out the superconformal block expansion and apply standard numerical bootstrap techniques in order to constrain the CFT data. We obtain bounds valid for any theory but also, thanks to input from the chiral algebra results, we are able to exclude solutions with mathcal{N}=4 supersymmetry,allowingustozoominonaspecific mathcal{N}=3 SCFT.

Highlights

The study of superconformal symmetry has given invaluable insights into quantum field theory, and in particular into the nature of strong-coupling dynamics
The problem is considered from two fronts: the protected subsector described by a 2d chiral algebra, and crossing symmetry for half-BPS operators whose superconformal primaries parametrize the Coulomb branch of N = 3 theories
With the goal of describing a protected subsector of a family of N = 3 superconformal field theories (SCFTs), we propose a new 2d chiral algebra with super Virasoro symmetry that depends on an arbitrary parameter, identified with the central charge of the theory

Summary

Introduction

The study of superconformal symmetry has given invaluable insights into quantum field theory, and in particular into the nature of strong-coupling dynamics. There is a significant amount of evidence that superconformal theories are not restricted to just Lagrangian examples, and this has inspired recent papers that revisit the status of N = 3 SCFTs. there is a significant amount of evidence that superconformal theories are not restricted to just Lagrangian examples, and this has inspired recent papers that revisit the status of N = 3 SCFTs Assuming these theories exist, the authors of [1] studied several of their properties. The authors of [1] studied several of their properties They found in particular that the a and c anomaly coefficients are always the same, that pure N = 3 theories (i.e., theories whose symmetry does not enhance to N = 4) have no marginal deformations and are always isolated, and in stark contrast with the most familiar N = 2 theories, that pure N = 3 SCFTs cannot have a flavor symmetry that is not an R-symmetry.

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