# In quest of a generalized Callias index theorem

## TL;DR

This paper proposes a new method using exponential regulators to compute the Callias index, confirms known results in odd dimensions, and suggests applications to moduli space dimension problems in even-dimensional loop spaces.

## Contribution

It introduces a novel exponential regulator approach for the Callias index and extends the index problem framework to moduli spaces in loop spaces.

## Key findings

- Agreement with known results in all odd dimensions
- Formulation of moduli space dimension as an index problem in loop space
- Potential applicability of the regulator to new index problems

## Abstract

We give a prescription for how to compute the Callias index, using as regulator an exponential function. We find agreement with old results in all odd dimensions. We show that the problem of computing the dimension of the moduli space of self-dual strings can be formulated as an index problem in even-dimensional (loop-)space. We think that the regulator used in this Letter can be applied to this index problem.