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

TL;DR

This paper calculates the free energy of large Nf QED in 2+1 dimensions across all coupling strengths, revealing finite results after resummation and providing insights into the theory's behavior at finite temperature.

Contribution

It presents the first next-to-leading-order large Nf calculation of free energy in 2+1D QED, including resummation of higher-order contributions for all coupling regimes.

Findings

Finite free energy well-behaved for all couplings.

Resummation renders UV-divergent contributions finite.

Free energy bounded by free fermions and non-interacting QED3.

Abstract

In 2+1 dimensions, QED becomes exactly solvable for all values of the fermion charge $e$ in the limit of many fermions $N_f\gg 1$. We present results for the free energy density at finite temperature $T$ to next-to-leading-order in large $N_f$. In the naive large $N_f$ limit, we uncover an apparently UV-divergent contribution to the vacuum energy at order ${\cal O}(e^6 N_f^3)$, which we argue to become a finite contribution of order ${\cal O}(N_f^4 e^6)$ when resumming formally higher-order $1/N_f$ contributions. We find the finite-temperature free energy to be well-behaved for all values of the dimensionless coupling $e^2N_f/T$, and to be bounded by the free energy of $N_f$ free fermions and non-interacting QED3, respectively. We invite follow-up studies from finite-temperature lattice gauge theory at large but fixed $N_f$ to test our results in the regime $e^2N_f/T\gg 1$.