Mean field quantization of effective string

TL;DR

This paper explores a mean-field quantization approach for bosonic strings, revealing differences from traditional methods, including a modified string susceptibility index and maintained conformal invariance in the mean-field approximation.

Contribution

It introduces a mean-field quantization method for bosonic strings, showing how it differs from classical vacuum quantization and preserves conformal invariance.

Findings

String susceptibility index $oldsymbol{_{str}}$ is 1/2 in mean-field approximation for 2<d<26

Total central charge equals zero in the mean-field approximation

Fluctuations do not break conformal invariance in the mean-field approach

Abstract

I describe the recently proposed quantization of bosonic string about the mean-field ground state, paying special attention to the differences from the usual quantization about the classical vacuum which turns out to be unstable for d>2. In particular, the string susceptibility index $\gamma_{\rm str}$ is 1 in the usual perturbation theory, but equals 1/2 in the mean-field approximation that applies for 2<d<26. I show that the total central charge equals zero in the mean-field approximation and argue that fluctuations about the mean field do not spoil conformal invariance.