Non-Critical Bosonic String Corrections to the Black Hole Entropy

TL;DR

This paper computes quantum corrections to black hole entropy from non-critical bosonic string theory, demonstrating ultraviolet finiteness for dimensions greater than two due to modular invariance, and explores related issues in field theory.

Contribution

It provides the first calculation of black hole entropy corrections from non-critical bosonic strings, highlighting the role of modular invariance in ensuring ultraviolet finiteness.

Findings

Entropy is ultraviolet finite for D>2 due to modular invariance.

Entropy diverges in the infrared for D>2, and in both ultraviolet and infrared for D=2.

The study links modular invariance with the behavior of black hole entropy in string theory.

Abstract

We calculate the quantum corrections to the entropy of a very large black hole, coming from the theory of a $D$-dimensional, non-critical bosonic string. We show that, for $D >2$, as a result of modular invariance the entropy is ultraviolet finite, although it diverges in the infrared (while for $D=2$ the entropy contains both ultraviolet and infrared divergences). The issue of modular invariance in field theory, in connection with black-hole entropy, is also investigated.