# Complex poles and spectral function of Yang-Mills theory

## TL;DR

This paper explores the relationship between complex poles and the spectral function in Yang-Mills theory, revealing how these features relate to gluon confinement and non-perturbative phenomena.

## Contribution

It establishes a general relation between complex poles and spectral functions and applies it to a mass-deformed Yang-Mills model to analyze gluon propagator properties.

## Key findings

- Gluon propagator has complex conjugate or tachyonic poles.
- Gluon spectral function is negative, indicating confinement.
- Ghost propagator has at most one unphysical pole.

## Abstract

We derive general relationships between the number of complex poles of a propagator and the sign of the spectral function originating from the branch cut in the Minkowski region under some assumptions on the asymptotic behaviors of the propagator. We apply this relation to the mass-deformed Yang-Mills model with one-loop quantum corrections, which is identified with a low-energy effective theory of the Yang-Mills theory, to show that the gluon propagator in this model has a pair of complex conjugate poles or "tachyonic" poles of multiplicity two, in accordance with the fact that the gluon field has a negative spectral function, while the ghost propagator has at most one "unphysical" pole. Finally, we discuss implications of these results for gluon confinement and other non-perturbative aspects of the Yang-Mills theory.