Anomalous dimensions of scalar operators in QED 3
Shai Chester (Joseph Henry Laboratories, Princeton University, Princeton, NJ, 08544, USA); Silviu Pufu (Joseph Henry Laboratories, Princeton University, Princeton, NJ, 08544, USA)
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 ψ ¯ i ψ i ψ ¯ j ψ j $$ \left({\overline{\psi}}_i{\psi}^i\right)\left({\overline{\psi}}_j{\psi}^j\right) $$ and F μν F μν , which are the lowest dimension parity-even singlets. Our results suggest that these operators are irrelevant for all N > 1.
