Remark on modular weights in low-energy effective field theory from type II string theory

TL;DR

This paper examines how modular weights in low-energy effective theories derived from type II string theory can vary due to localized fluxes and curvature, affecting supersymmetry breaking parameters.

Contribution

It highlights the potential shifts in modular weights in magnetized D-brane models and their implications for supersymmetry breaking, providing insights into model differences.

Findings

Modular weights in type IIB models are typically -1/2.

Localized fluxes and curvature can shift modular weights in type IIA models.

These shifts influence sfermion masses but not physical Yukawa couplings.

Abstract

We revisit the modular weights in type IIB magnetized D-brane models. The simple analysis of wave function shows that the four-dimensional matter fields have the modular weight -1/2, but it may shift as one in type IIA intersecting D-brane models. For example, the localized gauge flux as well as the localized curvature can shift the modular weight in the magnetized D-brane models. Such corrections do not affect physical couplings such as physical Yukawa couplings. However, it leads to differences in supersymmetry breaking sfermion masses, which depend on the modular weights, although the $A$-term coefficients and the sum of sfermion masses squared seem to be the same between two models.