CONSTANT MAGNETIC-FIELD IN CLOSED STRING THEORY - AN EXACTLY SOLVABLEMODEL

We consider a simple model describing a closed bosonic string in a con stant magnetic field. Exact conformal invariance demands also the pres ence of a non-trivial metric and antisymmetric tenser (induced by the magnetic field). The model is invariant under target space duality in a compact Kaluza-Klein direction introduced to couple the magnetic fie ld. Like open string theory in a constant gauge field, or closed strin g theory on a torus, this model can be straightforwardly quantised 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 tran sition. We also construct heterotic string generalisations of this bos onic model in which the constant magnetic field is embedded either in the Kaluza-Klein or internal gauge group sector.