Two-loop mass anomalous dimension in reduced quantum electrodynamics and application to dynamical fermion mass generation

Abstract

We consider reduced quantum electrodynamics (RQED${}_{d_{\gamma },d_e}$) a model describing fermions in a $d_e$-dimensional space-time and interacting via the exchange of massless bosons in $d_{\gamma }$-dimensions ($d_e\le d_{\gamma }$). We compute the two-loop mass anomalous dimension, ${\gamma }_m$, in general RQED${}_{4,d_e}$ with applications to RQED${}_{4,3}$ and QED${}_4$. We then proceed on studying dynamical (parity-even) fermion mass generation in RQED${}_{4,d_e}$ by constructing a fully gauge-invariant gap equation for RQED${}_{4,d_e}$ with ${\gamma }_m$ as the only input. This equation allows for a straightforward analytic computation of the gauge-invariant critical coupling constant, ${\alpha }_c$, which is such that a dynamical mass is generated for ${\alpha }_r>{\alpha }_c$, where ${\alpha }_r$ is the renormalized coupling constant, as well as the gauge-invariant critical number of fermion flavours, $N_c$, which is such that ${\alpha }_c\to \infty$ and a dynamical mass is generated for $N<N_c$. For RQED${}_{4,3}$, our results are in perfect agreement with the more elaborate analysis based on the resolution of truncated Schwinger-Dyson equations at two-loop order. In the case of QED${}_4$, our analytical results (that use state of the art five-loop expression for ${\gamma }_m$) are in good quantitative agreement with those obtained from numerical approaches.

(v2) Published in JHEP, very minor typos corrected, no change in results. (v1) LaTeX file with feynMF package. 36 pages, 2 figures

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