On $C_J$ and $C_T$ in Conformal QED

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, $C_J^{\text{top}}$. We also show that some RG flows involving QED in $d=3$ obey $C_T^{\mathrm{UV}}>C_T^{\mathrm{IR}}$ and discuss possible implications of this inequality for the symmetry breaking at small values of $N$.

29 pages, 9 figures. v3: minor improvements, references added

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