Anomalous dimensions of scalar operators in $QE{D}_3$

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 $N>1$.

33 pages, 13 figures, v2 minor improvements, refs added

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