D-Brane Probes and Mirror Symmetry

TL;DR

This paper explores how mirror symmetry affects D-brane probe physics on K3 surfaces, revealing geometric models of quantum splitting and discussing mirror symmetry in three-dimensional gauge theories.

Contribution

It provides a detailed analysis of mirror symmetry's impact on D-branes for elliptically fibered K3 surfaces, including the transformation of singular fibers and implications for gauge theories.

Findings

Mirror can transform ADE singular fibers into sets of I_1 (II) fibers with equal Euler number.

Mirror symmetry provides a geometric model of quantum splitting phenomena.

Brief discussion on mirror symmetry in three-dimensional gauge theories.

Abstract

We study the effect of mirror symmetry for K3 surfaces on D-brane probe physics. The case of elliptically fibered K3 surfaces is considered in detail. In many cases, mirror can transform a singular fiber of Kodaira's type ADE into sets of singular fibers of type I_1 (II) with equal total Euler number, but vanishing contribution to the Picard number of the mirror surface. This provides a geometric model of quantum splitting phenomena. Mirror for three dimensional gauge theories, interchanging Fayet-Iliopoulos and mass terms, is also briefly discussed.