Fractional Degrees of Freedom at Infinite Coupling in Large ${N}_{f}$ QED in $2+1$ Dimensions
Abstract
I consider quantum electrodynamics with many electrons in 2+1 spacetime dimensions at finite temperature. The relevant dimensionless interaction parameter for this theory is the fine structure constant divided by the temperature. The theory is solvable at any value of the coupling, in particular for very weak (high temperature) and infinitely strong coupling (corresponding to the zero temperature limit). Concentrating on the photon, each of its physical degrees of freedom at infinite coupling only contributes half of the freetheory value to the entropy. These fractional degrees of freedom are reminiscent of what has been observed in other strongly coupled systems (such as N=4 SYM), and bear similarity to the fractional Quantum Hall effect, potentially suggesting connections between these phenomena. The results found for QED3 are fully consistent with the expectations from particlevortex duality.
 Authors:

 Univ. of Colorado, Boulder, CO (United States)
 Publication Date:
 Research Org.:
 Univ. of Colorado, Boulder, CO (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), Nuclear Physics (NP)
 OSTI Identifier:
 1579393
 Alternate Identifier(s):
 OSTI ID: 1593886
 Grant/Contract Number:
 SC0017905
 Resource Type:
 Published Article
 Journal Name:
 Physical Review Letters
 Additional Journal Information:
 Journal Volume: 123; Journal Issue: 24; Journal ID: ISSN 00319007
 Publisher:
 American Physical Society (APS)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; Finite temperature field theory; Lowerdimensional field theories; Quantum electrodynamics
Citation Formats
Romatschke, Paul. Fractional Degrees of Freedom at Infinite Coupling in Large Nf QED in 2+1 Dimensions. United States: N. p., 2019.
Web. doi:10.1103/PhysRevLett.123.241602.
Romatschke, Paul. Fractional Degrees of Freedom at Infinite Coupling in Large Nf QED in 2+1 Dimensions. United States. https://doi.org/10.1103/PhysRevLett.123.241602
Romatschke, Paul. Thu .
"Fractional Degrees of Freedom at Infinite Coupling in Large Nf QED in 2+1 Dimensions". United States. https://doi.org/10.1103/PhysRevLett.123.241602.
@article{osti_1579393,
title = {Fractional Degrees of Freedom at Infinite Coupling in Large Nf QED in 2+1 Dimensions},
author = {Romatschke, Paul},
abstractNote = {I consider quantum electrodynamics with many electrons in 2+1 spacetime dimensions at finite temperature. The relevant dimensionless interaction parameter for this theory is the fine structure constant divided by the temperature. The theory is solvable at any value of the coupling, in particular for very weak (high temperature) and infinitely strong coupling (corresponding to the zero temperature limit). Concentrating on the photon, each of its physical degrees of freedom at infinite coupling only contributes half of the freetheory value to the entropy. These fractional degrees of freedom are reminiscent of what has been observed in other strongly coupled systems (such as N=4 SYM), and bear similarity to the fractional Quantum Hall effect, potentially suggesting connections between these phenomena. The results found for QED3 are fully consistent with the expectations from particlevortex duality.},
doi = {10.1103/PhysRevLett.123.241602},
journal = {Physical Review Letters},
number = 24,
volume = 123,
place = {United States},
year = {2019},
month = {12}
}
https://doi.org/10.1103/PhysRevLett.123.241602
Web of Science
Works referenced in this record:
Coupling constant dependence in the thermodynamics of N = 4 supersymmetric YangMills theory
journal, November 1998
 Gubser, Steven S.; Klebanov, Igor R.; Tseytlin, Arkady A.
 Nuclear Physics B, Vol. 534, Issue 12
The large $N$ limit of superconformal field theories and supergravity
journal, January 1998
 Maldacena, Juan
 Advances in Theoretical and Mathematical Physics, Vol. 2, Issue 2
Is the Composite Fermion a Dirac Particle?
journal, September 2015
 Son, Dam Thanh
 Physical Review X, Vol. 5, Issue 3
Polylogarithm identities in a conformal field theory in three dimensions
journal, July 1993
 Sachdev, Subir
 Physics Letters B, Vol. 309, Issue 34
Foam diagram summation at finite temperature
journal, August 1998
 Drummond, I. T.; Horgan, R. R.; Landshoff, P. V.
 Nuclear Physics B, Vol. 524, Issue 3
Chiralsymmetry breaking in threedimensional electrodynamics
journal, May 1984
 Pisarski, Robert D.
 Physical Review D, Vol. 29, Issue 10
Critical Behavior in (2+1)Dimensional QED
journal, June 1988
 Appelquist, Thomas; Nash, Daniel; Wijewardhana, L. C. R.
 Physical Review Letters, Vol. 60, Issue 25
FiniteTemperature Conformal Field Theory Results for All Couplings: $\mathrm{O}(N)$ Model in $2+1$ Dimensions
journal, June 2019
 Romatschke, Paul
 Physical Review Letters, Vol. 122, Issue 23
On C J and C T in conformal QED
journal, August 2016
 Giombi, Simone; Tarnopolsky, Grigory; Klebanov, Igor R.
 Journal of High Energy Physics, Vol. 2016, Issue 8
More Abelian dualities in 2 + 1 dimensions
journal, January 2017
 Karch, Andreas; Robinson, Brandon; Tong, David
 Journal of High Energy Physics, Vol. 2017, Issue 1
Strong coupling universality at large N for pure CFT thermodynamics in 2+1 dimensions
journal, October 2019
 DeWolfe, Oliver; Romatschke, Paul
 Journal of High Energy Physics, Vol. 2019, Issue 10
Basics of Thermal Field Theory: A Tutorial on Perturbative Computations
book, January 2016
 Laine, Mikko; Vuorinen, Aleksi
 Lecture Notes in Physics (book series)
Quantum Hall physics: Hierarchies and conformal field theory techniques
journal, May 2017
 Hansson, T. H.; Hermanns, M.; Simon, S. H.
 Reviews of Modern Physics, Vol. 89, Issue 2
The LargeN Limit of Superconformal Field Theories and Supergravity
journal, January 1999
 Maldacena, Juan
 International Journal of Theoretical Physics, Vol. 38, Issue 4, p. 11131133
Deducing hard thermal loops from Ward identities
journal, July 1990
 Braaten, Eric; Pisarski, Robert D.
 Nuclear Physics B, Vol. 339, Issue 2
ParticleVortex Duality from 3D Bosonization
journal, September 2016
 Karch, Andreas; Tong, David
 Physical Review X, Vol. 6, Issue 3
New Measurement of the Electron Magnetic Moment Using a OneElectron Quantum Cyclotron
journal, July 2006
 Odom, B.; Hanneke, D.; D’Urso, B.
 Physical Review Letters, Vol. 97, Issue 3
${\mathrm{QED}}_{3}$ theory of pairing pseudogap in cuprates: From $d$ wave superconductor to antiferromagnet via an algebraic Fermi liquid
journal, August 2002
 Franz, M.; Tešanović, Z.; Vafek, O.
 Physical Review B, Vol. 66, Issue 5
Divergence of Perturbation Theory in Quantum Electrodynamics
journal, February 1952
 Dyson, F. J.
 Physical Review, Vol. 85, Issue 4
Pressure of Hot QCD at Large N _{f}
journal, October 2002
 Moore, Guy D.
 Journal of High Energy Physics, Vol. 2002, Issue 10
Comment on and erratum to ``Pressure of hot QCD at large N _{ f } ''
journal, January 2003
 Ipp, Andreas; Moore, Guy D.; Rebhan, Anton
 Journal of High Energy Physics, Vol. 2003, Issue 01