Prepotentials, Bi-linear Forms on Periods and Enhanced Gauge Symmetries in Type-II Strings

TL;DR

This paper constructs bi-linear forms on Calabi-Yau periods to derive prepotentials near conifold singularities in type-II string compactifications, revealing enhanced gauge symmetries and stringy corrections.

Contribution

It explicitly constructs bi-linear forms for one- and two-moduli Calabi-Yau models, linking them to flat coordinates and prepotentials with alpha' corrections.

Findings

Derived explicit prepotentials around conifold points.

Connected bi-linear forms with enhanced gauge symmetries.

Included stringy alpha' corrections in the prepotentials.

Abstract

We construct a bi-linear form on the periods of Calabi-Yau spaces. These are used to obtain the prepotentials around conifold singularities in type-II strings compactified on Calabi-Yau space. The explicit construction of the bi-linear forms is achieved for the one-moduli models as well as two moduli models with K3-fibrations where the enhanced gauge symmetry is known to be observed at conifold locus. We also show how these bi-linear forms are related with the existence of flat coordinates. We list the resulting prepotentials in two moduli models around the conifold locus, which contains alpha' corrections of 4-D N=2 SUSY SU(2) Yang-Mills theory as the stringy effect.