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

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.

arXiv comment7 Pages, 1 figure, Template changed, Additional citations added and corrected some typos

References in corpus (12)

• The Large N Limit of Superconformal Field Theories and Supergravity
• AdS/CFT Correspondence and Symmetry Breaking
• Bulk vs. Boundary Dynamics in Anti-de Sitter Spacetime
• The Operator Product Expansion for Wilson Loops and Surfaces in the Large N Limit
• Renormalization-Group Improved Effective Lagrangian for Interacting Theories in Curved Spacetime
• The 1-loop effective potential for the Standard Model in curved spacetime
• Effective Lagrangian for self-interacting scalar field theories in curved spacetime
• Effective Lagrangian and the back-reaction problem in a self-interacting $O(N)$ scalar theory in curved spacetime
• Rindler-AdS/CFT
• Symmetry Restoration By Acceleration
• Triggering the QCD phase transition through the Unruh effect: chiral symmetry restoration for uniformly accelerated observers
• Free energy and entropy in Rindler and de Sitter space-times

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• Fluid Acceleration in Heavy-Ion Collisions
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