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High Energy Physics - Theory
Title: Beyond $N=\infty$ in Large $N$ Conformal Vector Models at Finite Temperature
(Submitted on 5 Sep 2023 (v1), last revised 22 Apr 2024 (this version, v2))
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.
Submission history
From: Oleksandr Diatlyk [view email][v1] Tue, 5 Sep 2023 16:03:47 GMT (147kb,D)
[v2] Mon, 22 Apr 2024 21:12:20 GMT (199kb,D)
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