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 $e^2{N}_f/T\gg 1$.

arXiv comment17 pages, 1 figure; comments welcome

References in corpus (25)

• The Large N Limit of Superconformal Field Theories and Supergravity
• Shear viscosity of strongly coupled N=4 supersymmetric Yang-Mills plasma
• Supergravity and The Large N Limit of Theories With Sixteen Supercharges
• Coupling Constant Dependence in the Thermodynamics of N=4 Supersymmetric Yang-Mills Theory
• Is the Composite Fermion a Dirac Particle?
• Basics of thermal field theory -- a tutorial on perturbative computations
• Particle-Vortex Duality from 3d Bosonization
• QED3 theory of pairing pseudogap in cuprates: From d-wave superconductor to antiferromagnet via "algebraic" Fermi liquid
• Advances in perturbative thermal field theory
• Quantum criticality of U(1) gauge theories with fermionic and bosonic matter in two spatial dimensions
• Non-compact QED_3 with N_f >=2
• More Abelian Dualities in 2+1 Dimensions
• Foam Diagram Summation at Finite Temperature
• No evidence for bilinear condensate in parity-invariant three-dimensional QED with massless fermions
• On $C_J$ and $C_T$ in Conformal QED
• Comment on and Erratum to "Pressure of Hot QCD at Large N_f"
• Pressure of Hot QCD at Large N_f
• 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
• Phase Structure of Compact $QE{D}_3$ with Massless Fermions
• 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
• Massless QED_3 with explicit fermions
• Fractionalized Degrees of Freedom at Infinite Coupling in large Nf QED in 2+1 dimensions
• Effective Coupling Constant of Plasmons

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• Duality Constraints on Thermal Spectra of 3d Conformal Field Theories and 4d Quasinormal Modes