New Ideas in Symmetry Breaking

TL;DR

This paper reviews various mechanisms of symmetry breaking in theories with extra dimensions, focusing on compactification methods, boundary conditions, and Wilson lines, and their applications to particle physics symmetries.

Contribution

It provides a comprehensive overview of symmetry breaking techniques in extra-dimensional models, including recent developments and detailed analysis of mechanisms like Scherk-Schwarz and Hosotani breaking.

Findings

Comparison of compactification mechanisms

Application to supersymmetry and gauge symmetry breaking

Illustrated with relevant examples

Abstract

Some old and new ideas on symmetry breaking, based on the presence of extra dimensions that have been the subject of a very fast development and intensive studies during the last years, will be presented in these lectures. Special attention will be devoted to the various compactification mechanisms, including toroidal and orbifold compactifications, and to non-trivial boundary conditions or Scherk-Schwarz compactification. Also symmetry breaking by Wilson lines, or Hosotani breaking characteristic of non-simply connected compact manifolds will be analyzed in some detail. The different mechanisms will be applied to the breaking of the most relevant symmetries in particle physics: supersymmetry and gauge symmetry. The required background for these lectures is Quantum Field Theory, Supersymmetry and some rudiments of Kaluza-Klein theory. The different sections will be illustrated with examples.