Open and Closed String Vertices for branes with magnetic field and T-duality

TL;DR

This paper analyzes open and closed string vertices on magnetized D-branes, revealing how T-duality and magnetic flux influence string interactions, and demonstrates the equivalence of T-dual theories including gravitational effects.

Contribution

It provides a detailed study of string vertices with magnetic flux, showing how T-duality preserves the open string sector and deriving the boundary state in magnetic backgrounds.

Findings

Closed string vertices acquire Chan-Paton matrices due to translation invariance.

One-loop amplitudes have a single trace for gauge groups with magnetic flux.

T-duality relates open string theories with magnetic flux, including gravitational interactions.

Abstract

We discuss carefully the vertices which describe the dipole open strings and closed strings on a D-brane with magnetic flux on a torus. Translation invariance along closed cycles forces surprisingly closed string vertices written in open string formalism to acquire Chan-Paton like matrices. Moreover the one loop amplitudes have a single trace for the part of gauge group with the magnetic flux. These peculiarities are also required by consistency of the action of T-duality in the open string sector. In this way we can show to all orders in perturbation theory the equivalence of the T-dual open string theories, gravitational interactions included. We provide also a new and direct derivation of the bosonic boundary state in presence of constant magnetic and Kalb-Ramond background based on Sciuto-Della Selva-Saito vertex formalism.