Evaluation of Periods via Fibrations in Seiberg-Witten Theories and in Type-II String

TL;DR

This paper develops methods to evaluate periods in Seiberg-Witten theories and K3-fibered Calabi-Yau manifolds using fibrations, revealing connections between string theory and gauge theory.

Contribution

It introduces a unified approach to compute periods in complex theories using fibrations, linking string compactifications with gauge theory solutions.

Findings

Constructed dual pairs of fields from classical fields in Seiberg-Witten theories.

Derived solutions of Picard-Fuchs equations for K3-fibered Calabi-Yau manifolds.

Connected string theory periods to SU(2) Seiberg-Witten theory.

Abstract

We show how to evaluate the periods in Seiberg-Witten theories and in K3-fibered Calabi-Yau manifolds by using fibrations of the theories. In the Seiberg-Witten theories, it is shown that the dual pair of fields can be constructed from the classical fields in a simple form. As for Calabi-Yau manifolds which are fibrations of K3 surface, we obtain the solutions of the Picard-Fuchs equations from the periods of K3 surface. By utilizing the expression of periods for two-parameter models of type-II string, we derive the solutions of the Picard-Fuchs equations around the points of enhanced gauge symmetry and show a simple connection to the SU(2) Seiberg-Witten theory.