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

Abstract

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).

Interacting CFTs for all couplings: Thermal versus Entanglement Entropy at Large $N$

“…therm (T, λ) matches the bosonic contribution of the entropy density of a Nambu-Jona-Lasinio-Yukawa model given in Ref. [9]. Considering equation (2.9), the gap equation at infinite coupling is,…”

“…Further, applying this generalized theory to 2 + 1d produces a strong-to-weak thermal entropy density ratio of 4 5 , matching results of quartic and sextic theories in Refs. [4][8] and [9]. In Ref.…”

Determining all thermodynamic transport coefficients for an interacting large N quantum field theory

“…Going forward, we expect that our results may be generalized to calculate thermodynamic transport coefficients for all quantum field theories that are 'solvable' in the large N limit, in particular also in other dimensions [45], with fermions [46], supersymmetric theories [47] and for certain tensor theories, cf. [48].…”

Shear Viscosity at Infinite Coupling: A Field Theory Calculation

“…In addition to serving as a well-defined test bed for general-purpose tools, the present calculation may be generalized in several ways. By, for instance, calculating other transport coefficients such as the bulk viscosity ζ as well as relaxation time τ π for the O(N) model; calculating transport coefficients for other large N theories [33][34][35]; calculating exact far-from equilibrium real-time dynamics at large N for a quantum field theory.…”

“…(59), (60). Using the orthogonal polynomials defined for the quadrature (34), it is convenient to parametrize The values of A nm are calculated numerically.…”