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arXiv · 1603.05582

Anomalous dimensions of scalar operators in $QED_3$

Shai M. Chester·Silviu S. Pufu
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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 $N>1$.

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Shai M. Chester, Silviu S. Pufu. 2016-03-17. Anomalous dimensions of scalar operators in $QED_3$. https://doi.org/10.1007/jhep08(2016)069

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