D-branes in Singular Calabi-Yau n-fold and N=2 Liouville Theory

TL;DR

This paper investigates D-branes wrapped around vanishing cycles in singular Calabi-Yau n-folds using N=2 Liouville theory, deriving properties like intersection numbers and scaling behavior consistent with geometry.

Contribution

It constructs boundary states for wrapped D-branes and analyzes their properties using world-sheet techniques, providing new insights into their geometric and physical characteristics.

Findings

Derived holomorphicity and scaling behavior of vanishing cycles.

Calculated intersection numbers matching geometric expectations.

Analyzed open string Witten index in the context of singular Calabi-Yau spaces.

Abstract

Making use of the N=2 Liouville theory and world-sheet techniques, we study the properties of D-branes wrapped around vanishing SUSY cycles of singular Calabi-Yau n-folds (n=2,3,4). After constructing boundary states describing the wrapped branes, we evaluate the disc amplitudes corresponding to the periods of SUSY cycles. We use the old technique of KPZ scaling in Liouville theory and derive holomorphicity and scaling behavior of vanishing cycles which are in agreement with geometrical considerations. We also discuss the open string Witten index using the N=2 Liouville theory and obtain the intersection numbers among SUSY cycles which also agree with geometrical expectation.