Magnetised Bounds for Conformal Field Theories

TL;DR

This paper develops a framework for analyzing three-dimensional parity-preserving conformal field theories with a global U(1) symmetry under magnetic fields, deriving universal bounds and predictions for their responses and operator dimensions.

Contribution

It constructs a four-derivative effective action for such CFTs in magnetic backgrounds and derives universal constraints on response functions and operator scaling dimensions.

Findings

Universal bounds on Wilson coefficients of the effective action.

Predictions for CFT response at large magnetic fields.

Scaling dimensions of background monopole operators.

Abstract

Aspects of parity-preserving, three-dimensional conformal field theories (CFTs) with a global $U(1)$ symmetry in the presence of a background magnetic field are investigated. A local effective action is constructed to four-derivative order, based on an assumption that the magnetic field drives the theory into a gapped phase. This action is evaluated in a variety of backgrounds, and is used to obtain one- and two-point functions of the conserved current and stress-energy tensor. Dispersive arguments are developed and shown to impose powerful constraints on the Wilson coefficients of the effective action, leading to universal predictions for the CFT response at large magnetic field and the scaling dimensions of background monopole operators. These general results are further examined through explicit calculations in the free complex scalar, free Dirac fermion, and a holographic Einstein-Hilbert-Maxwell model.