String Stars in Anti de Sitter Space

Abstract

We study the 'string star' saddle, also known as the Horowitz-Polchinski solution, in the middle of d + 1 dimensional thermal AdS space. We show that there's a regime of temperatures in which the saddle is very similar to the flat space solution found by Horowitz and Polchinski. This saddle is hypothetically connected at lower temperatures to the small AdS black hole saddle. We also study, numerically and analytically, how the solutions are changed due to the AdS geometry for higher temperatures. Specifically, we describe how the solution joins with the thermal gas phase, and find the leading correction to the Hagedorn temperature due to the AdS curvature. Finally, we study the thermodynamic instabilities of the solution and argue for a Gregory-Laflamme-like instability whenever extra dimensions are present at the AdS curvature scale.

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

“…This result was first derived in [17,18]. Using (4.3) and d = 4 this gives T H = g 2π + 1 2π + O(g −1/2 ) which fits with the numerical results eqs.…”

“…Recently, important advances have been made on the string theory side, with the discovery that the so-called thermal scalar can compute not just the leading order flat-space temperature at infinite coupling, but also the first order correction [17,18], giving T H ≃ g 2π + 1 2π , for large g, which matches the results of [11,15]. Indeed, we can write the thermal scalar equation of motion (EOM) as…”

“…The first order correction to the flat-space Hagedorn temperature was computed in [17,18] using the thermal scalar equation. In this case we consider the leading order approximation of the l.h.s.…”

“…One can argue for this by employing a modular transformation of the torus string amplitude [22,23]. For type IIB string theory on AdS 5 × S 5 , the thermal scalar EOM (1.1) captures the above-mentioned leading term and the first-order correction to T H [17,18]. Relative to the leading piece, the first-order correction is proportional to l s /R ∼ 1/ √ g where R is the curvature length scale of the background.…”