Supersymmetric zeta functions and determinants

TL;DR

This paper introduces supersymmetric zeta functions and determinants that provide new spectral insights, aiding the analysis of supersymmetric indices and energies across various dimensions.

Contribution

It defines novel supersymmetric spectral functions and explores their applications in understanding supersymmetric partition functions and energies.

Findings

Supersymmetric zeta functions reveal spectral properties beyond indices.

These functions help analyze Cardy-like behaviors in supersymmetric theories.

Examples include applications in 2D, 4D, and 6D supersymmetric field theories.

Abstract

We define supersymmetric zeta functions and supersymmetric determinants, which can reveal spectral properties complementary to those captured by the supersymmetric indices. They play a crucial role in analyzing the Cardy-like behaviors of the supersymmetric indices and the supersymmetric Casimir energies associated with the supersymmetric partition functions. We investigate a variety of examples of the supersymmetric zeta functions and determinants for two-, four-, and six-dimensional supersymmetric field theories.