Index for Three Dimensional Superconformal Field Theories and Its Applications

TL;DR

This paper reviews the computation of superconformal indices in three-dimensional theories, highlighting their applications in dualities, holography, and symmetry enhancement, with a focus on exact localization methods including monopole effects.

Contribution

It provides a comprehensive review of superconformal index calculations in 3D and explores the potential for symmetry enhancement in finite gauge groups.

Findings

Superconformal indices can be exactly computed using localization including monopole contributions.

Indices provide evidence for mirror duality and AdS_4/CFT_3 correspondence.

Discussion on the possibility of global symmetry enhancement in finite gauge groups.

Abstract

We review aspects of superconformal indices in three dimension. Three dimensional superconformal indices can be exactly computed by using localization method including monopole contribution, and can be applied to provide evidences for mirror duality, AdS_4/CFT_3 correspondence and global symmetry enhancement of strongly coupled gauge theories. After reviewing, we discuss the possibility of global symmetry enhancement in a finite rank of gauge group.