From Type IIA Black Holes to T-dual Type IIB D-Instantons in N=2, D=4 Supergravity

TL;DR

The paper investigates how T-duality between type IIA and type IIB strings on a Calabi–Yau threefold is realized in four-dimensional N=2 supergravity through the c-map, which exchanges the vector multiplet (special Kähler) moduli with hypermultiplet (quaternionic) moduli. By mapping known IIA black-hole solutions to IIB D-instanton solutions, the authors construct a broad class of D-instantons in D=4 that are determined by harmonic functions and topological CY data, including detailed treatment of the universal sector and double-extreme cases. They provide explicit dualities for ten-dimensional brane configurations, derive the corresponding four-dimensional Lagrangians, and show how the quaternionic structure of hypermultiplets governs the IIB instanton dynamics. The findings illuminate non-perturbative effects in CY compactifications, connect BH entropy to D-instanton geometry via attractor-like mechanisms, and offer a framework for exploring instanton corrections in N=2 theories with CY moduli.

Abstract

We discuss the T-duality between the solutions of type IIA versus IIB superstrings compactified on Calabi-Yau threefolds. Within the context of the N=2, D=4 supergravity effective Lagrangian, the T-duality transformation is equivalently described by the c-map, which relates the special Kahler moduli space of the IIA N=2 vector multiplets to the quaternionic moduli space of the N=2 hyper multiplets on the type IIB side (and vice versa). Hence the T-duality, or c-map respectively, transforms the IIA black hole solutions, originating from even dimensional IIA branes, of the special Kahler effective action, into IIB D-instanton solutions of the IIB quaternionic sigma-model action, where the D-instantons can be obtained by compactifying odd IIB D-branes on the internal Calabi-Yau space. We construct via this mapping a broad class of D-instanton solutions in four dimensions which are determinded by a set of harmonic functions plus the underlying topological Calabi-Yau data.