Super Picard-Fuchs equation and monodromies for supermanifolds

Abstract

Following, Aganagic and Vafa (e-print hep-th/0403192) and Hori and Vafa (e-print hep-th/0002222), we discuss the Picard-Fuchs equation for the super Landau-Ginsburg mirror to the super Calabi-Yau in WC P(3|2) [1,1,1,3|1,5] (using techniques of Greene and Lazaroiu [Nucl. Phys. B 604, 181 (2001), e-print hep-th/0001025] and Misra [Fortschr. Phys. 52, 831 (2004), e-print hep-th/0311186]), Meijer basis of solutions, and monodromies (at 0,1 and ∞) in the large and small complex structure limits, as well as obtain the mirror hypersurface, which in the large Kähler limit turns out to be either a bidegree-(6,6) hypersurface in WC P(3|1) [1,1,1,2] ×WC P(1|1) [1,1|6] or a (Z2 singular) bidegree-(6,12) hypersurface in WC P(3|1) [1,1,2,6|6] ×WC P(1|1) [1,1|6]. © 2007 American Institute of Physics.