Boundary Conformal Field Theory at Large Charge

Understand

We study operators with large internal charge in boundary conformal field theories (BCFTs) with internal symmetries.

• Using the state-operator correspondence and the existence of a macroscopic limit, we find a non-trivial relation between the scaling dimension of the lowest dimensional CFT and BCFT charged operators to leading order in the charge.
• We also construct the superfluid effective field theory for theories with boundaries and use it to systematically calculate the BCFT spectrum in a systematic expansion.
• We verify explicitly many of the predictions from the EFT analysis in concrete examples including the classical conformal scalar field with a $|\phi|^6$ interaction in three dimensions and the $O(2)$ Wilson-Fisher model near four dimensions in the presence of boundaries.