Thermal free energy of large Nf 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 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.

Shear Viscosity at Infinite Coupling: A Field Theory Calculation

“…Hence in the infinite coupling limit the result for the shear viscosity for (36) is identical to that of (4). It is not hard to generalize this proof to theories with other interactions φ a φ a → U (φ a φ a ) for a large class of potentials U (x), which demonstrates that (35) is the universal strong coupling shear viscosity over entropy ratio for a large class of bosonic QFTs. The same universal behavior was found [16] for the weak-strong ratio s λ=∞ s λ=0 = 4 5 and for the boson in-medium mass lim λ→∞ m = 2 ln 1+ √ 5…”

“…In this work, I derived an exact large N expression for the ratio of shear viscosity over entropy density for the interacting O(N) model, using well-established field theory techniques. Evaluating the expression numerically in the case of 2+1 dimensions, I found the strong coupling result (35). While my analytic skills are not sufficient for this undertaking, it would be interesting to check if this large N strong coupling result is η s = 3N 4π or not.…”

“…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.…”

Hydrodynamic dispersion relations at finite coupling

“…kinetic) regime in the same theory. This interpolation, even for simplest theories such as CFTs considered at finite temperature, is not fully understood [16,33,36,[48][49][50][51][52]. Admittedly, relying -even only qualitatively -on the non-perturbative treatment in models arising as truncations of a perturbative expansion may seem to be unwarranted [34].…”

$\mathrm{U(1)}$ and $\mathbb{Z}_2$ spin liquids on the pyrochlore lattice

“…A finite temperature calculation can also be considered following Ref. [43]. We leave such a calculation to future work.…”