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 $N_f\gg 1$. 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 $\mathcal{O}(e^6{N}_f^3)$, which we argue to become a finite contribution of order $\mathcal{O}(N_f^4{e}^6)$ 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 $e^2{N}_f/T$, 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 $e^2{N}_f/T\gg 1$.

17 pages, 1 figure; comments welcome

References in corpus (8)

• Quantum criticality of U(1) gauge theories with fermionic and bosonic matter in two spatial dimensions
• More Abelian Dualities in 2+1 Dimensions
• Non-perturbative beta function in three-dimensional electrodynamics
• Simple non-perturbative resummation schemes beyond mean-field: case study for scalar ${\varphi }^4$ theory in 1+1 dimensions
• Analytic Transport from Weak to Strong Coupling in the O(N) model
• Finite temperature CFT results for all couplings: O(N) model in 2+1 dimensions
• Fractionalized Degrees of Freedom at Infinite Coupling in large Nf QED in 2+1 dimensions
• Effective Coupling Constant of Plasmons

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