Hagedorn temperature from the thermal scalar in AdS and pp-wave backgrounds

In the context of the black hole/string transition, it is useful to produce Euclidean string backgrounds representing hot and self-gravitating strings. We utilise analytical and numerical methods to find a smooth, stationary rotating solution in the heterotic string theory at high temperatures. The solution describes a spinning winding-momentum condensate living in three non-compact dimensions, and its backreaction on the thermal cycle. At low temperatures, we expect a transition between our solution to an analytical continuation of an axionic Kerr black hole.

Self gravitating spinning string condensates

Santos,

Zigdon

2024

Hagedorn temperature in holography: world-sheet and effective approaches

Bigazzi,

Canneti,

Castellani

et al. 2024

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 α′; 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.

On the asymptotic density of states in solvable models of strings

Canneti

2024