On Superparticles and their Partition Functions

TL;DR

This paper introduces a family of twisted partition functions for relativistic spinning particles, revealing their connection to physical state counting, BV-spectrum encoding, and potential space-time action formulations.

Contribution

It presents novel twisted partition functions that refine Euler characteristics and encode the complete BV-spectrum for relativistic spinning particles.

Findings

Partition functions compute physical state dimensions.

They encode the complete BV-spectrum of the gauge theory.

Off-shell and on-shell descriptions are provided.

Abstract

We describe a family of twisted partition functions for the relativistic spinning particle models. For suitable choices of fugacities this computes a refined Euler characteristics that counts the dimension of the physical states for arbitrary picture and, furthermore, encodes the complete BV-spectrum of the effective space-time gauge theory originating from this model upon second quantization. The relation between twisted world-line partition functions and the spectrum of the space-time theory is most easily seen on-shell but we will give an off-shell description as well. Finally we discuss the construction of a space-time action in terms of the world-line fields in analogy to string field theory.