Spontaneously Broken Boosts in CFTs

Understand

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.