Random Walks in Rindler Spacetime and String Theory at the Tip of the Cigar

TL;DR

This paper explores string thermodynamics in Rindler spacetime, modeling the behavior of long strings near black hole horizons and connecting field theory, random walks, and string theory insights.

Contribution

It provides a detailed analysis of string thermodynamics at the black hole horizon, demonstrating the dominance of long strings and linking different approaches including the cigar model.

Findings

Long strings dominate thermodynamics near the horizon.

Random walk picture effectively models string behavior.

Agreement with the cigar model and flat space orbifold approaches.

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 JHEP 1402 (2014) 127. 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 string-scale 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).