The twisted open string partition function and Yukawa couplings

TL;DR

This paper derives a new method to compute Yukawa couplings in D-brane models using twisted open string partition functions and Prym differentials, offering an alternative to traditional stress-energy tensor techniques.

Contribution

It introduces an operator formalism approach to calculate twisted open string partition functions and Yukawa couplings, providing explicit formulas for the g=2 case on a 2-torus.

Findings

Explicit expression for the 3-twist field correlator

Alternative computation method for Yukawa couplings

Application to magnetized or intersecting D-branes

Abstract

We use the operator formalism to derive the bosonic contribution to the twisted open string partition function in toroidal compactifications. This amplitude describes, for instance, the planar interaction between g+1 magnetized or intersecting D-branes. We write the result both in the closed and in the open string channel in terms of Prym differentials on the appropriate Riemann surface. Then we focus on the g=2 case for a 2-torus. By factorizing the twisted partition function in the open string channel we obtain an explicit expression for the 3-twist field correlator, which is the main ingredient in the computation of Yukawa couplings in D-brane phenomenological models. This provides an alternative method for computing these couplings that does not rely on the stress-energy tensor technique.