On $C_{J}$ and $C_{T}$ in Conformal QED

TL;DR

This paper calculates leading corrections to key conformal data in large N QED across various dimensions, providing explicit formulas and exploring implications for RG flows and symmetry breaking.

Contribution

It offers explicit formulas for $C_T$ and $C_J$ in conformal QED across dimensions, including higher derivatives and topological currents, extending previous results.

Findings

Derived formulas for $C_T$ and $C_J$ as functions of dimension $d$.

Calculated corrections to topological current two-point functions in $d=3$.

Observed RG flow inequalities suggesting symmetry breaking scenarios.

Abstract

QED with a large number $N$ of massless fermionic degrees of freedom has a conformal phase in a range of space-time dimensions. We use a large $N$ diagrammatic approach to calculate the leading corrections to $C_T$, the coefficient of the two-point function of the stress-energy tensor, and $C_J$, the coefficient of the two-point function of the global symmetry current. We present explicit formulae as a function of $d$ and check them versus the expectations in 2 and $4-\epsilon$ dimensions. Using our results in higher even dimensions we find a concise formula for $C_T$ of the conformal Maxwell theory with higher derivative action $F_{\mu \nu} (-\nabla^2)^{\frac{d}{2}-2} F^{\mu \nu}$. In $d=3$, QED has a topological symmetry current, and we calculate the correction to its two-point function coefficient, $C^{\textrm{top}}_{J}$. We also show that some RG flows involving QED in $d=3$ obey $C_T^{\rm UV} > C_T^{\rm IR}$ and discuss possible implications of this inequality for the symmetry breaking at small values of $N$.