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

Romatschke, Paul; Säppi, Matias

doi:10.1103/PhysRevD.100.073009

Title: Thermal free energy of large $N_{f}$ QED in $2 + 1$ dimensions from weak to strong coupling

Journal Article · Tue Oct 22 00:00:00 EDT 2019 · Physical Review. D.

DOI:https://doi.org/10.1103/PhysRevD.100.073009· OSTI ID:1571337

Romatschke, Paul;

In 2+1 dimensions, QED becomes exactly solvable for all values of the fermion charge e in the limit of many fermions $N_{f}$ >> 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 O(e⁶N$$^{3}_{f}$$/ε), which we argue would become a finite contribution of order O(e⁶N$$^{4}_{f}$$) when resumming formally higher-order 1/ $N_{f}$ contributions. Still in the limit of large $N_{f}$ , 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 $N_{f}$ 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 $N_{f}$ to test our results in the regime e² $N_{f}$ /T >> 1.

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Research Organization:: Univ. of Colorado, Boulder, CO (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Nuclear Physics (NP)

Grant/Contract Number:: SC0017905

OSTI ID:: 1571337

Alternate ID(s):: OSTI ID: 1593888

Journal Information:: Physical Review. D., Journal Name: Physical Review. D. Vol. 100 Journal Issue: 7; ISSN 2470-0010

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 5 works

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Title: Thermal free energy of large N f QED in 2 + 1 dimensions from weak to strong coupling

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Title: Thermal free energy of large $N_{f}$ QED in $2 + 1$ dimensions from weak to strong coupling