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

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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.