BPS states and their reductions

TL;DR

This paper introduces a method to identify BPS states in supersymmetric theories on curved spaces and establishes a correspondence between these states and lower-dimensional partition functions, enabling new computational techniques.

Contribution

It develops a novel approach to connect BPS states with lower-dimensional partition functions and applies this to compute superconformal indices on various three-spheres.

Findings

Derived superconformal indices on rounded and squashed three spheres

Established a one-to-one correspondence between BPS states and lower-dimensional states

Demonstrated the reduction of indices to exact partition functions

Abstract

We develop a method to identify the BPS states in the Hilbert space of a supersymmetric field theory on a generic curved space which preserves at least two real supercharges. We also propose a one-to-one map between BPS states in d-dimensional field theories and states that contribute to the supersymmetric partition function of a corresponding (d-1)-dimensional field theory. As an application we obtain the superconformal index on rounded and squashed three spheres, and we show a natural reduction of the respective indices to the three-dimensional exact partition functions. We discuss the validity of the correspondence both at the perturbative and at the non-perturbative level and exploit the idea to uplift the computation of the exact supersymmetric partition function on a general manifold to a higher dimensional index.