Duality in Superstring Compactifications with Magnetic Field Backgrounds

TL;DR

This paper investigates how magnetic fields in heterotic string compactifications affect vacuum stability and supersymmetry, revealing conditions under which tachyonic states stabilize the vacuum and exploring duality implications.

Contribution

It provides a detailed analysis of tachyonic states and Landau levels in heterotic string compactifications with magnetic fields, including explicit CFT descriptions and duality insights.

Findings

Tachyonic states can stabilize the vacuum by acquiring VEVs.

Landau levels influence the potential and vacuum structure.

Explicit CFT descriptions for toroidal and orbifold examples.

Abstract

Motivated by the work of Polchinski and Strominger on type IIA theory, where the effect of non-trivial field strengths for p-form potentials on a Calabi-Yau space was discussed, we study four-dimensional heterotic string theory in the presence of magnetic field on a 2-cycle in the internal manifold, for both N=4 and N=2 cases. We show that at special points in the moduli space, certain perturbative charged states become tachyonic and stabilize the vacuum by acquiring vacuum expectation values, thereby restoring supersymmetry. We discuss both the cases where the tachyons appear with a tower of Landau levels, which become light in the limit of large volume of the 2-cycle, and the case where such Landau levels are not present. In the latter case it is sufficient to restrict the analysis to the quartic potential for the tachyon. On the other hand, in the former case it is necessary to include the Landau levels in the analysis of the potential; for toroidal and orbifold examples, we give an explicit CFT description of the new supersymmetric vacuum. The resulting new vacuum turns out to be in the same class as the original supersymmetric one. Finally, using duality, we discuss the role of the Landau levels on the type IIA side.