Spontaneously Broken Spacetime Symmetries and Goldstone's Theorem

TL;DR

This paper explains how to get the right count of massless modes in the general case, and discusses examples involving spontaneously broken Poincaré and conformal invariance.

Abstract

Goldstone's theorem states that there is a massless mode for each broken symmetry generator. It has been known for a long time that the naive generalization of this counting fails to give the correct number of massless modes for spontaneously broken spacetime symmetries. We explain how to get the right count of massless modes in the general case, and discuss examples involving spontaneously broken Poincare and conformal invariance.

Figures (1)

• Figure 1: A ground state with a string breaks the three-dimensional Poincaré group down to the two-dimensional Poincaré group. Global translation and rotation on the string are distinctly different, whereas the effects of local translation and rotation on the string can be made the same.