# Interplay between $SU(N_f)$ chiral symmetry, $U(1)_A$ axial anomaly and massless bosons

## TL;DR

This paper explores how topological properties and the $U(1)_A$ axial anomaly can generate massless bosons in gauge theories with fermions, offering an alternative to the traditional symmetry-breaking explanation, with implications for QCD and early universe physics.

## Contribution

It proposes a novel mechanism linking topological features and the axial anomaly to massless boson emergence in chiral symmetric vacua, supported by analysis of the Schwinger model and implications for high-temperature QCD.

## Key findings

- Topological properties can induce massless bosons without symmetry breaking.
- Validation using the two-flavour Schwinger model in the strong-coupling limit.
- Implications for the high-temperature phase of QCD in the early universe.

## Abstract

The standard wisdom on the origin of massless bosons in the spectrum of a Quantum Field Theory $(QFT)$ describing the interaction of gauge fields coupled to matter fields is based on two well known features: gauge symmetry, and spontaneous symmetry breaking of continuous global symmetries. However we will show in this article how the topological properties, that originate the $U(1)_A$ axial anomaly in a $QFT$ which describes the interaction of fermion matter fields and gauge bosons, are the basis of an alternative mechanism to generate massless bosons in the chiral limit, if the non-abelian $SU(N_f)_A$ chiral symmetry is fulfilled in the vacuum. We will also test our predictions with the results of a well known two-dimensional model, the two-flavour Schwinger model, which was analyzed by Coleman long ago, and will give a reliable answer to some of the questions he asked himself on the spectrum of the model in the strong-coupling (chiral) limit. We will also analyze what are the expectations for the $U(N)$ gauge-fermion model in two dimensions, and will discuss on the impact of our results in the chirally symmetric high temperature phase of $QCD$, which was present in the early universe, and is expected to be created in heavy-ion collision experiments.