Random walks in Rindler spacetime and string theory at the tip of the cigar

Abstract

In this paper, we discuss Rindler space string thermodynamics from a thermal scalar point of view as an explicit example of the results obtained in [1]. We discuss the critical behavior of the string gas and interpret this as a random walk near the black hole horizon. Combining field theory arguments with the random walk path integral picture, we realize (at genus one) the picture put forward by Susskind of a long string surrounding black hole horizons. We find that thermodynamics is dominated by a long string living at stringscale distance from the horizon whose redshifted temperature is the Rindler or Hawking temperature. We provide further evidence of the recent proposal for string theory at the tip of the cigar by comparing with the flat space orbifold approach to Rindler thermodynamics. We discuss all types of closed strings (bosonic, type II and heterotic strings).

Perturbative string thermodynamics near black hole horizons

“…In particular we argue that a truncation to the oneloop thermodynamics of only the massless modes is incapable of approximating the one-loop string result. Then in section 4, we discuss Rindler space for the heterotic string, a problem that was left open in [1]. We noted there that it appears that the thermal scalar action for the heterotic string in Euclidean Rindler space without any α -corrections is capable of reproducing expected results.…”

“…1 Non-extremal black holes on the other hand are (in spite of several influential ideas) still largely understood on a qualitative level only. The main line of thought that pervades the literature on this topic is the idea that a long string(s) should give the necessary microstructure to such black holes.…”

“…In [1] we combined thermal scalar field theory computations with the explicit random walk picture of the long string [17,18] to provide a realization of Susskind's picture in the canonical ensemble. We arrived at the conclusion that the Hawking temperature equals the Hagedorn temperature and hence in this sense the long string phase prevails.…”

“…Section 2 contains a review of the results presented in [1] in which we will provide more details on the puzzles that were left open in that work. Then, as an appetizer, in section 3 we discuss the role and relevance of long strings in one-loop black hole thermodynamics.…”

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Abstract:We provide further computations and ideas to the problem of near-Hagedorn string thermodynamics near (uncharged) black hole horizons, building upon our earlier work [1]. The relevance of long strings to one-loop black hole thermodynamics is emphasized.

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