Anomalous dimensions of scalar operators in $QED_3$

TL;DR

This paper uses the 1/N expansion to compute the scaling dimensions of scalar operators in 2+1 dimensional QED with many flavors, providing insights into their relevance in the infrared conformal field theory.

Contribution

It calculates the anomalous dimensions of specific scalar operators in QED$_3$ using the 1/N expansion, including operator mixing for singlets, which was not previously detailed.

Findings

Operators are irrelevant for all N > 1.

Computed scaling dimensions for operators transforming under SU(N).

Analyzed mixing of singlet operators involving fermions and gauge fields.

Abstract

The infrared dynamics of $2+1$ dimensional quantum electrodynamics (QED$_3$) with a large number $N$ of fermion flavors is governed by an interacting CFT that can be studied in the $1/N$ expansion. We use the $1/N$ expansion to calculate the scaling dimensions of all the lowest three scalar operators that transform under the $SU(N)$ flavor symmetry as a Young diagram with two columns of not necessarily equal heights and that have vanishing topological charge. In the case of $SU(N)$ singlets, we study the mixing of $(\bar \psi_i \psi^i)(\bar \psi_j \psi^j)$ and $F_{\mu\nu} F^{\mu\nu}$, which are the lowest dimension parity-even singlets. Our results suggest that these operators are irrelevant for all $N>1$.