On Aspects of Spontaneous Symmetry Breaking in Rindler and Anti-de Sitter spacetimes for the $O(N)$ Linear Sigma Model

TL;DR

This paper studies spontaneous symmetry breaking in the $O(N)$ linear sigma model within Rindler and Anti-de Sitter spacetimes, revealing phase transitions influenced by acceleration and spacetime dimensionality.

Contribution

It provides a large $N$ analysis of symmetry breaking in curved spacetimes, connecting Rindler space with finite temperature effects and exploring dimensional dependence in Anti-de Sitter space.

Findings

Phase transition in Rindler space at critical acceleration.

Symmetry broken in AdS3 but not in AdS4.

Rindler space acts as a finite temperature proxy.

Abstract

We investigate aspects of spontaneous breakdown of symmetry for $O(N)$ symmetric linear sigma model in the background of Rindler and Anti-de Sitter spacetimes respectively. In the large $N$ limit, by computing the one-loop effective action, we report that in three dimensional Rindler space, there is a phase transition from the disordered phase to an ordered phase past a certain critical Rindler acceleration parameter `$a$'. Connections with finite temperature field theory results are established, thereby further reinforcing the idea that Rindler space can indeed be a proxy for Minkowski spacetime with finite temperature. We extend our calculations to Anti-de Sitter space in various dimensions and observe that symmetry is broken in three dimensions, but not in four dimensions. We discuss the implications of our results.