On the Hagedorn temperature in holographic confining gauge theories

Abstract

The divergence of the string partition function due to the exponential growth of states is a well-understood issue in flat spacetime. It can be interpreted as the appearance of tachyon modes above a certain temperature, known as the Hagedorn temperature TH. In the literature, one can find some intuitions about its generalization to curved spacetimes, where computations are extremely hard and explicit results cannot be provided in general. In this paper, we present a genus-zero estimate of TH, at leading order in α′, for string theories on curved backgrounds holographically dual to confining gauge theories. This is a particularly interesting case, since the holographic correspondence equates TH with the Hagedorn temperature of the dual gauge theories. For concreteness we focus on Type IIA string theory on a well known background dual to an SU(N) Yang-Mills theory. The resulting Hagedorn temperature turns out to be proportional to the square root of the Yang-Mills confining string tension. The related coefficient, which at leading order is analytically determined, is the same as the one for Type II theories in flat space. While the calculation is performed in a specific model, the result applies in full generality to confining gauge theories with a top-down holographic dual.

Higher order corrections to the Hagedorn temperature at strong coupling

“…Consider a quadratic world-sheet theory of eight bosons with masses m 2 B,i = a 2 i µ 2 , i = 1, . .…”

“…In recent months, the determination of the Hagedorn temperature T H [1] in string backgrounds has found renewed interest. In [2][3][4], the authors address the problem in supergravity solutions dual to confining gauge theories, both with a world-sheet method and with an effective approach inspired by the Horowitz-Polchinski construction [5]. The latter has been also applied to exact backgrounds as AdS 5 × S 5 [6].…”

Semiclassical quantization of the superstring and Hagedorn temperature

“…This work is motivated by the recent paper [1] by two of us and A. L. Cotrone, in which the semiclassical quantization of a closed string winding once around the compact Euclidean time direction and sitting in a nearly flat region of Witten's type-IIA supergravity background [2], was considered. The region was chosen to holographically correspond to the deep infrared regime of the confining phase of the dual SU(N ) gauge theory, henceforth called Witten-Yang-Mills (WYM) theory.…”

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In a recent paper [1], the semiclassical quantization of a string, winding once around the compact Euclidean time circle, on a supergravity background dual to the deep infrared regime of a confining finite temperature gauge theory, was carried out. The string mass-shell condition and, by extrapolation, the Hagedorn temperature to leading order in the holographic limit was deduced.

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Nonlinear Regge trajectories and saturation of the Hagedorn spectrum

“…In our analyses, we rely on the latest results of the Particle Data Group [6]. At the same time, we are aware of recent important developments and progress in theoretical studies of the Hagedorn spectrum and of the ultimate temperature based on gauge theories [7], lattice QCD (by which one distinguishes between two different types of resonances: isolated ones in vacuum, and resonance at a certain temperature), strings, supergravity [8][9][10]. Its possible manifestation in the early universe was discussed in Refs.…”