Spectral dimension of bosonic string theory

TL;DR

This paper calculates the spectral dimension of closed bosonic string theory, finding it to be 26, which contrasts with the 2 predicted by many quantum gravity approaches in the ultraviolet regime.

Contribution

It provides a direct computation of the spectral dimension for bosonic string theory, revealing a significant difference from other quantum gravity models.

Findings

Spectral dimension of bosonic string theory is 26.

Most quantum gravity approaches predict spectral dimension 2 in UV.

Implications of the disparity between string theory and other models are discussed.

Abstract

Given that the scale of quantum gravity is not experimentally accessible, one naturally resorts to mathematical consistency as a measure for a good candidate theory to replace General Relativity at high energies. Reproducing the semi-classical results of black hole entropy has become a standard test for any prospective theory of quantum gravity. It is often argued that another such commonality, albeit less known, is the similar fractal behaviour. It is shown that many, if not all, approaches to quantum gravity predict a spectral dimension of 2 in ultraviolet regime. In this paper, by computing the heat kernel, we show that the spectral dimension of closed bosonic string theory is 26. We discuss the implications of this disparity.