Coset Techniques and Hunt for Wess-Zumino Terms

Abstract

The coset construction is a mathematical tool that extends usual representation theory to non-linear representations of symmetries on fields. It is ideal for building low-energy Effective Field Theories (EFTs) for systems that exhibit Spontaneous Symmetry Breaking (SSB) and was originally used to construct the pion Lagrangian. The speaker will show how its extension to SSB of spacetime symmetries can describe numerous systems from condensed matter to cosmology. A few entertaining examples will be given - for example, he will show that rigid body mechanics can be derived from a coset construction.

He will then present two recent extensions to the coset construction: First, the construction of Wess-Zumino (WZ) terms for the EFT. WZ terms are required for the complete low-energy description and have the interesting feature that they can lead to anomalies when the symmetries are gauged. He will show that WZ terms only depend on the SSB pattern and present an algorithm that constructs them. Second, he will discuss how to gauge the Poincaré group in the coset construction, thereby coupling the Goldstone bosons to gravity. This can be used for example to describe relativistic spinning objects such as neutron stars or black holes.

About the program

For details, please visit the program website at http://iasprogram.ust.hk/particle_theory.