Spontaneously Broken Boosts in CFTs

TL;DR

This paper explores how spontaneously broken boost and dilatation symmetries in conformal field theories impose constraints, leading to new low-lying primaries and affecting the spectrum in various heavy states.

Contribution

It introduces the constraints from spontaneously broken boost symmetries in CFTs and analyzes their implications across different physical states and models.

Findings

Broken boost symmetries imply existence of low-lying primaries with O(1) scaling dimension gap.

Constraints are demonstrated in fluid, superfluid, mean field, and Fermi surface states.

Remarks on large charge limit in 2d and conformal anomaly effects are included.

Abstract

Conformal Field Theories (CFTs) have rich dynamics in heavy states. We describe the constraints due to spontaneously broken boost and dilatation symmetries in such states. The spontaneously broken boost symmetries require the existence of new low-lying primaries whose scaling dimension gap, we argue, scales as $O(1)$. We demonstrate these ideas in various states, including fluid, superfluid, mean field theory, and Fermi surface states. We end with some remarks about the large charge limit in 2d and discuss a theory of a single compact boson with an arbitrary conformal anomaly.