Modular Zeros

TL;DR

This paper explores the structure of vector-valued modular forms and introduces the concept of modular zeros, which help explain stringy zeros and the Weinberg texture relating quark hierarchies.

Contribution

It identifies modular zeros as gaps in VVMF spaces that elucidate certain string theory zeros and quark mass textures.

Findings

Modular zeros correspond to gaps in VVMF spaces.

Modular zeros explain stringy zeros.

They clarify the Weinberg texture linking quark hierarchies.

Abstract

Modular symmetries are known to be powerful and have various remarkable properties. We point out that the structure of vector-valued modular forms (VVMFs) space leads to the absence of couplings which cannot be explained in terms of the usual symmetries. These modular zeros, which correspond to gaps in spaces of VVMFs, have the power of explaining certain stringy zeros, and to explain the renowned Weinberg texture that relates the Cabibbo angle to the hierarchies of the light down and strange quarks.