# Stability of the nonperturbative bosonic string vacuum

## TL;DR

This paper investigates the stability of a nonperturbative mean field vacuum in bosonic string theory across various spacetime dimensions, demonstrating its stability and drawing parallels with sigma-models.

## Contribution

It extends the mean field analysis of the bosonic string vacuum to finite dimensions and establishes its stability under quadratic fluctuations.

## Key findings

- Mean field vacuum is stable for 2<d<26
- Analogy with the O(N)-sigma-model's 1/N-vacuum
- Contrasts with perturbative vacuum stability

## Abstract

Quantization of the bosonic string around the classical, perturbative vacuum is not consistent for spacetime dimensions 2<d<26. Recently we have showed that at large d there is another so-called mean field vacuum. Here we extend this mean field calculation to finite d and show that the corresponding mean field vacuum is stable under quadratic fluctuations for 2<d<26. We point out the analogy with the two-dimensional O(N)-symmetric sigma-model, where the 1/N-vacuum is very close to the real vacuum state even for finite N, in contrast to the perturbative vacuum.