Boundary Conformal Field Theory at Large Charge

TL;DR

This paper investigates the behavior of large-charge operators in boundary conformal field theories, deriving relations between operator dimensions and constructing effective theories to analyze spectra systematically.

Contribution

It introduces a superfluid effective field theory for BCFTs with boundaries and systematically computes the spectrum, verifying predictions in specific models.

Findings

Derived a relation between scaling dimensions of operators and charge in BCFTs.

Constructed a superfluid EFT for boundary theories and calculated spectra.

Validated EFT predictions with examples like the conformal scalar and O(2) models.

Abstract

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. In the appendices we additionally discuss a systematic background field approach towards Ward identities in general boundary and defect conformal field theories, and clarify its relation with Noether's theorem in perturbative theories.