Open Strings in Magnetic Background Fields

Abstract

We discuss various aspects of internal magnetic background fields in open string theories. Phenomenologically and conceptually interesting properties of such string theory backgrounds, supersymmetry and gauge symmetry breaking, chiral fermion spectra and noncommutativity of the internal compactification manifolds, are treated in a rather generic framework. We then specialize to type I compactifications on tori and toroidal orbifolds with magnetic fields on the internal space. This allows to develop a strategy for constructing type I vacua with attractive low energy field theories which may either be supersymmetric or not and contain chiral spectra and gauge groups close to the Standard Model or some grand unified generalization thereof. The most sophisticated version uses magnetic fields and NSNS B‐fields on orbifold spaces giving rise to a plethora of promising examples for semi‐realistic string compactifications. We finally also present a related class of asymmetric orbifolds of type I which are of little phenomenological interest but still display certain interesting features. The asymmetric rotations which are gauged in these models identify D‐branes with different values for the magnetic field on their world volume, such that the distinction of commutative and noncommutative internal geometries is lost.

On closed-string twist-field correlators and their open-string descendants

“…with p and q being integers and p 2 open denoting the open string mass. For a D1-brane wrapping a one-cycle on a two torus the mass is given by [36,37]…”

“…Concerning the quantum part one expects only the holomorphic part to survive. Finally the mass of the open strings in the untwisted sector is given by [36,37]…”

Orientifolds of K3 and Calabi-Yau Manifolds with Intersecting D-branes

“…In the case of orbifold realizations mirror symmetry is simply given by T-duality along three of the six compact directions which maps a symmetric Z Z N orbifold to an asymmetric Ẑ Z N orbifold. Moreover, intersecting D6-branes are mapped to D9-branes with constant magnetic flux as has been studied in [1,73,131].…”

Intersecting brane worlds on tori and orbifolds

“…The idea dates back, in a dual disguise, to the work [1] which was the first to realize explicitly, that certain magnetic background fields can break supersymmetry, together with chiral and gauge symmetry. It was then embedded into string theory for toroidal and orbifold background spaces [2,3] and generalized to include also the NSNS B field modulus [4,5] (see also [6] for a review). The background fluxes, when interpreted as a constant background for open string propagation, induce a modification of the standard Dirichlet boundary conditions, which maps to the boundary conditions of rotated D-branes [7] under T-duality.…”

“…The four-dimensional couplings relevant for the GS mechanism descend from C (2) ∧ tr F 4 and C (6) ∧ tr F 2 , leading to an anomalous contribution schematically given by…”