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Title: Thermal free energy of large N f 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 >> 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(e 6N$$^{3}_{f}$$/ε), which we argue would become a finite contribution of order O(e 6N$$^{4}_{f}$$) 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 e 2 N f /T >> 1.

Authors:
 [1]; ORCiD logo [2]
  1. Univ. of Colorado, Boulder, CO (United States)
  2. Univ. of Helsinki (Finland)
Publication Date:
Research Org.:
Univ. of Colorado, Boulder, CO (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26)
OSTI Identifier:
1571337
Alternate Identifier(s):
OSTI ID: 1593888
Grant/Contract Number:  
SC0017905
Resource Type:
Published Article
Journal Name:
Physical Review D
Additional Journal Information:
Journal Volume: 100; Journal Issue: 7; Journal ID: ISSN 2470-0010
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
73 NUCLEAR PHYSICS AND RADIATION PHYSICS; Conformal field theory; Finite temperature field theory; Large-N expansion in field theory; Lower-dimensional field theories; Quantum electrodynamics

Citation Formats

Romatschke, Paul, and Säppi, Matias. Thermal free energy of large Nf QED in 2+1 dimensions from weak to strong coupling. United States: N. p., 2019. Web. doi:10.1103/PhysRevD.100.073009.
Romatschke, Paul, & Säppi, Matias. Thermal free energy of large Nf QED in 2+1 dimensions from weak to strong coupling. United States. doi:10.1103/PhysRevD.100.073009.
Romatschke, Paul, and Säppi, Matias. Tue . "Thermal free energy of large Nf QED in 2+1 dimensions from weak to strong coupling". United States. doi:10.1103/PhysRevD.100.073009.
@article{osti_1571337,
title = {Thermal free energy of large Nf QED in 2+1 dimensions from weak to strong coupling},
author = {Romatschke, Paul and Säppi, Matias},
abstractNote = {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(e6N$^{3}_{f}$/ε), which we argue would become a finite contribution of order O(e6N$^{4}_{f}$) 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.},
doi = {10.1103/PhysRevD.100.073009},
journal = {Physical Review D},
number = 7,
volume = 100,
place = {United States},
year = {2019},
month = {10}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: 10.1103/PhysRevD.100.073009

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