Hagedorn temperature in holography: world-sheet and effective approaches

TL;DR

This paper investigates the Hagedorn temperature in holographic confining gauge theories using world-sheet and effective field theory methods, providing precise calculations up to high orders and insights into the thermal scalar's properties.

Contribution

It offers the first detailed derivation of the fermionic world-sheet spectrum and computes the Hagedorn temperature up to NNNLO in complex holographic backgrounds.

Findings

Hagedorn temperature determined up to NNNLO for exact backgrounds

Derived the fermionic part of the world-sheet spectrum in detail

Connected world-sheet and effective field theory approaches for thermal scalar

Abstract

We provide general results on the Hagedorn temperature of planar, strongly coupled confining gauge theories holographically dual to type II superstring models on curved backgrounds with Ramond-Ramond and Kalb-Ramond fluxes and non-trivial dilaton. For exact backgrounds the Hagedorn temperature is determined up to next-to-next-to-next-to-leading order (NNNLO) in an expansion in $\alpha'$; in all the other cases the results can be safely trusted up to NNLO. To reach these goals we exploit two complementary approaches. On the one hand, we perform an extrapolation to the Hagedorn regime of world-sheet results obtained from the semiclassical quantization of string configurations winding around the compact Euclidean time direction. En passant, we provide a detailed derivation of the fermionic part of the world-sheet spectrum, which is hard to find in the literature. On the other hand, we perturbatively solve the equations of motion for the thermal scalar field corresponding to the lightest mode of the winding string, which in flat space becomes tachyonic above the Hagedorn temperature. The interplay between different approaches is surely convenient, but we provide insights about a possible derivation of the whole NNLO correction to the Hagedorn temperature from a pure world-sheet perspective; furthermore, we determine the effective mass of the thermal scalar from the world-sheet in full generality.