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We consider massless three-dimensional $\mathcal{N}=1$ supersymmetric quantumelectrodynamics (QED) with $N_f$ flavours of electrons. Within the dimensionalreduction scheme, we compute the critical exponents corresponding to both theelectron and selectron field and (parity-even) mass anomalous dimensions at thenext-to-leading order in the $1/N_f$ expansion and in an arbitrary covariantgauge. The equality of the gauge-invariant mass anomalous dimensions of theelectron and the selectron is found to result from a subtle role played by theepsilon-scalars. Our general framework also allows us to compute the criticalexponents of pure scalar QED and to recover known results in the case of spinorQED. An application of our results to dynamical (s)electron mass generation isconsidered. We find evidence that, while dynamical flavor symmetry breakingoccurs in spinor QED, both pure scalar QED and supersymmetric QED remain in aninteracting conformal phase.

Electron mass anomalous dimension at $O(1/N_f^2)$ in three-dimensional $\mathcal{N}=1$ supersymmetric QED