Beyond $N=\infty$ in Large $N$ Conformal Vector Models at Finite Temperature

TL;DR

This paper analyzes finite-temperature effects in large N conformal vector models, including subleading 1/N corrections, and explores their impact on thermodynamic quantities, symmetries, and higher-spin currents.

Contribution

It provides explicit 1/N corrections to free energy and stress-energy tensor one-point functions, and determines the Wilson coefficient for the first time in interacting CFTs.

Findings

Subleading effects lift degeneracies between models at infinite N.

Explicit formulas for thermal one-point functions of higher-spin currents.

Dependence on chemical potential and symmetry-resolved density of states.

Abstract

We investigate finite-temperature observables in three-dimensional large $N$ critical vector models taking into account the effects suppressed by $1\over N$. Such subleading contributions are captured by the fluctuations of the Hubbard-Stratonovich auxiliary field which need to be handled with care due to a subtle divergence structure which we clarify. The examples we consider include the scalar $O(N)$ model, the Gross-Neveu model, the Nambu-Jona-Lasinio model and the massless Chern-Simons Quantum Electrodynamics. We present explicit results for the free energy density to the subleading order in $1\over N$, which captures the thermal one-point function of the stress-energy tensor to this order. We also include the dependence on a chemical potential. We determine the Wilson coefficient in the thermal effective action that is sensitive to global symmetry for the first time directly in interacting CFTs, which produces a symmetry-resolved asymptotic density of states. We further provide a formula from diagrammatics for the one-point functions of general single-trace higher-spin currents. We observe that in most cases considered, these subleading effects lift the apparent degeneracies between observables in different models at infinite $N$, while in special cases the discrepancies only start to appear at the next-to-subleading order.