New twist field couplings from the partition function for multiply wrapped D-branes

TL;DR

This paper computes multi-loop partition functions for multiply wrapped D-branes on tori, revealing how cocycles influence unitarity and enabling the calculation of twist field couplings relevant for string phenomenology.

Contribution

It introduces a method to derive 3-point twist field couplings on generic tori from multi-loop partition functions, extending previous results beyond simple 2-tori.

Findings

Partition functions depend critically on cocycles for unitarity.

Derived explicit 3-point couplings for abelian twist fields on non-factorized tori.

Connected multi-loop partition functions to tree-level twist field correlators.

Abstract

We consider toroidal compactifications of bosonic string theory with particular regard to the phases (cocycles) necessary for a consistent definition of the vertex operators, the boundary states and the T-duality rules. We use these ingredients to compute the planar multi-loop partition function describing the interaction among magnetized or intersecting D-branes, also in presence of open string moduli. It turns out that unitarity in the open string channel crucially depends on the presence of the cocycles. We then focus on the 2-loop case and study the degeneration limit where this partition function is directly related to the tree-level 3-point correlators between twist fields. These correlators represent the main ingredient in the computation of Yukawa couplings and other terms in the effective action for D-brane phenomenological models. By factorizing the 2-loop partition function we are able to compute the 3-point couplings for abelian twist fields on generic non-factorized tori, thus generalizing previous expressions valid for the 2-torus.