Magnetic flux tube models in superstring theory

TL;DR

This paper analyzes superstring models with magnetic flux tube backgrounds, demonstrating their stability, supersymmetry breaking, and the conditions under which instabilities occur, with exact solutions and connections to known string theories.

Contribution

It provides exact solvable superstring models with magnetic flux tubes, exploring supersymmetry breaking, stability conditions, and the relation to free string theories at special parameters.

Findings

Models are perturbatively stable for R > R_0

Supersymmetry is broken due to non-trivial connections in fermionic terms

Instabilities appear for R < R_0 and certain magnetic field strengths

Abstract

Superstring models describing curved 4-dimensional magnetic flux tube backgrounds are exactly solvable in terms of free fields. We first consider the simplest model of this type (corresponding to `Kaluza-Klein' Melvin background). Its 2d action has a flat but topologically non-trivial 10-dimensional target space (there is a mixing of angular coordinate of the 2-plane with an internal compact coordinate). We demonstrate that this theory has broken supersymmetry but is perturbatively stable if the radius R of the internal coordinate is larger than R_0=\sqrt{2\a'}. In the Green-Schwarz formulation the supersymmetry breaking is a consequence of the presence of a flat but non-trivial connection in the fermionic terms in the action. For R < R_0 and the magnetic field strength parameter q > R/2\a' there appear instabilities corresponding to tachyonic winding states. The torus partition function Z(q,R) is finite for R > R_0 (and vanishes for qR=2n, n=integer). At the special points qR=2n (2n+1) the model is equivalent to the free superstring theory compactified on a circle with periodic (antiperiodic) boundary condition for space-time fermions. Analogous results are obtained for a more general class of static magnetic flux tube geometries including the a=1 Melvin model.