D-branes in singular Calabi-Yau n-fold and N=2 Liouville theory

Making use of the N = 2 Liouville theory and world-sheet techniques, we stu dy the properties of D-branes wrapped around vanishing SUSY cycles of singu lar Calabi-Yau n-folds (n = 2, 3, 4). After constructing boundary states de scribing the wrapped branes, we evaluate the disc amplitudes corresponding to the periods of SUSY cycles. We use the old technique of KPZ scaling in L iouville 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 theo ry and obtain the intersection numbers among SUSY cycles which also agree w ith geometrical expectation. (C) 2001 Elsevier Science B.V. All rights rese rved.