Strong coupling universality at large N for pure CFT thermodynamics in 2+1 dimensions

The massless three-dimensional Gross-Neveu-Yukawa (GNY) and Nambu-Jona-Lasinio-Yukawa (NJLY) models at finite temperatures are analyzed within the mean field framework considering all coupling values. When the number of Dirac fermions is taken to be N f ¼ 1=4 (GNY) and N f ¼ 1=2 (NJLY) these models relate to the supersymmetric Wess-Zumino (WZ) theory with cubic superpotential and one superfield. In this case the results show that the strong-weak entropy density ratio decreases from the Stefan-Boltzmann value, in the weak limit, to s=s free ¼ 31=35 at strong couplings. This value agrees with the one recently obtained by applying the large-N approximation to the supersymmetric OðNÞ WZ model with quartic superpotential and N superfields. When N f ¼ 0 one obtains s=s free ¼ 4=5 recovering, as expected, the ratio predicted in the context of the OðNÞ scalar model. However, contrary to the OðNÞ WZ model the simple Yukawa models analyzed here do not behave as CFTs for all couplings since the conformal measure exactly vanishes only at the extreme weak and strong limits although the speed of sound indicates that the deviation, at intermediate couplings, appears to be rather small. By comparing the thermal masses behavior in each case one can trace this difference as being a consequence that in the GNY/NJLY case the fermionic mass vanishes for all couplings while within the OðNÞ WZ it only vanishes at the weak and strong limits. On the other hand, the Yukawa bosonic dimensionless masses display a more universal behavior decreasing from 2 ln½ð1 þ ffiffi ffi 5 p Þ=2, at infinite coupling, to zero (at vanishing coupling).

Section: The Yukawa Modelsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

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Three-dimensional Yukawa models and CFTs at strong and weak couplings

Pinto

2020

“…Note that the speed of sound is very close to (and above) the conformal result c 2 s = 1 3 , which indicates that the O(N) model, though not a conformal theory (CFT), is numerically very close to a CFT for most coupling values. Indeed, it has not escaped my attention that the ratio s/s free calculated from (20) seems to go to a constant value of approximately 85 percent for λ R → ∞ and χ = 1, very much in line with the universal strong-weak thermodynamic behavior found in 2+1d CFTs [22,24].…”

mentioning

confidence: 72%

Analytic transport from weak to strong coupling in the O(N) model

Romatschke

2019

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In this work, a second-order transport coefficient (the curvature-matter coupling κ) is calculated exactly for the 3+1d O(N) model at large N for any coupling value. Since the theory is "trivial" in the sense of possessing a Landau pole, the result for κ only is free from cut-off artifacts much below the Landau pole in the effective field theory sense. Nevertheless, this leaves a large range of coupling values where this transport coefficient can be determined non-perturbatively and analytically with little ambiguity. Along with thermodyamic results also calculated in this work, I expect exact large N results to provide good quantitative predictions for N=1 scalar field theory with φ 4 interaction.

“…At first glance, this project seems to be dead on arrival: if techniques existed to, say, solve QCD non-perturbatively, using gaugegravity dual results for N = 4 super-Yang-Mills theory as a proxy for QCD would not have been needed. Surprisingly, however, a number of large N quantum field theories can be solved at finite temperature for all values of the coupling, including scalar field theories [5][6][7], Wess-Zumino models [7] and Gross-Neveu models, albeit in two spatial dimensions (2+1d).…”

Section: Introductionmentioning

confidence: 99%

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

Romatschke

Säppi

2019

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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 6 N 3 f ), which we argue to become a finite contribution of order O(e 6 N 4 f ) 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 1.