Holographic thermal propagator for arbitrary scale dimensions

Using the AdS/CFT correspondence we model the behaviour of the two point correlator of an operator with arbitrary scale dimension $\mathrm{\Delta }$ 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 $\mathrm{\Delta }$ 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 $\mathrm{\Delta }$, and present a conjecture for the order $T^{2d}$ in the large $\mathrm{\Delta }$ limit.