# Extracting topological information from momentum space propagators

## TL;DR

This paper introduces a new gauge-invariant topological invariant based on momentum space propagators, capable of classifying complex poles and potentially detecting phenomena like chiral symmetry breaking and deconfinement.

## Contribution

A novel topological invariant sensitive to propagator structures is proposed, extending to complex poles and applicable in non-perturbative quantum field theory contexts.

## Key findings

- Invariant can classify propagators with complex poles
- Potential to detect chiral symmetry breaking
- May identify deconfinement transitions

## Abstract

A new topological invariant quantity, sensitive to the analytic structure of both fermionic and bosonic propagators, is proposed. The gauge invariance of our construct is guaranteed for at least small gauge transformations. A generalization compatible with the presence of complex poles is introduced and applied to the classification of propagators typically emerging from non-perturbative considerations. We present partial evidence that the topological number can be used to detect chiral symmetry breaking or deconfinement.