Constant magnetic field in closed string theory: an exactly solvable model

TL;DR

This paper presents an exactly solvable model of a closed bosonic string in a constant magnetic field, revealing a phase transition at high field strength and extending to heterotic strings with embedded magnetic fields.

Contribution

It introduces a new exactly solvable model of closed string theory in a magnetic field, including its spectrum, duality properties, and heterotic generalizations.

Findings

Spectrum explicitly computed and shown to include tachyons above critical magnetic field

Model exhibits target space duality symmetry

Heterotic string extensions constructed with magnetic field embedded in gauge sectors

Abstract

We consider a simple model describing a closed bosonic string in a constant magnetic field. Exact conformal invariance demands also the presence of a non-trivial metric and antisymmetric tensor (induced by the magnetic field). The model is invariant under target space duality in a compact Kaluza-Klein direction introduced to couple the magnetic field. Like open string theory in a constant gauge field, or closed string theory on a torus, this model can be straightforwardly quantized and solved with its spectrum of states and partition function explicitly computed. Above some critical value of the magnetic field an infinite number of states become tachyonic, suggesting a presence of phase transition. We also construct heterotic string generalisations of this bosonic model in which the constant magnetic field is embedded either in the Kaluza-Klein or internal gauge group sector.