Thermal free energy of large Nf QED in 2+1 dimensions from weak to strong coupling

Abstract

In 2+1 dimensions, QED becomes exactly solvable for all values of the fermion charge e in the limit of many fermions Nf≫1. We present results for the free energy density at finite temperature T to next-to-leading-order in large Nf. In the naive large Nf limit, we uncover an apparently UV-divergent contribution to the vacuum energy at order O(e6Nf3ϵ), which we argue would become a finite contribution of order O(e6Nf4) when resumming formally higher-order 1/Nf contributions. Still in the limit of large Nf, we find the finite-temperature free energy to be well-behaved for all values of the dimensionless coupling e2Nf/T, and to be bounded from above by the free energy of Nf free fermions and bounded from below by non-interacting QED3. We invite follow-up studies from finite-temperature lattice gauge theory at large but fixed Nf to test our results in the regime e2Nf/T≫1.