Holographic thermal propagator for arbitrary scale dimensions

TL;DR

This paper derives a holographic model for two-point correlators of operators with arbitrary scale dimension in various spacetime dimensions at small non-zero temperature, extending known results and proposing new conjectures.

Contribution

It provides a generalized holographic propagator for arbitrary scale dimensions and spacetime dimensions at finite temperature, including explicit formulas and conjectures for higher-order temperature effects.

Findings

Matches known low-temperature results for specific cases

Provides explicit order T^d propagator expressions for arbitrary dimensions and scale dimensions

Proposes a conjecture for order T^{2d} in the large scale dimension limit

Abstract

Using the AdS/CFT correspondence we model the behaviour of the two point correlator of an operator with arbitrary scale dimension $\Delta$ in arbitrary spacetime dimension $d$ for small but non-zero temperature. The obtained propagator coincides in the low temperature regime with the known result for $d=4$ for large $\Delta$ at the order $T^d$ as well as with the $T^d$ and $T^{2d}$ terms of the exact all order result for $d=2$. Furthermore, for arbitrary $d$ we explicitly write down the expression for the order $T^{d}$ of the propagator for arbitrary $\Delta$, and present a conjecture for the order $T^{2d}$ in the large $\Delta$ limit.