D-instantons and twistors: some exact results

TL;DR

The paper develops an all-orders twistor-space description of nonperturbative D2-instanton corrections to the Type II hypermultiplet moduli space, extending previous linear results. It provides an exact single-charge construction and a full, symplectically consistent framework for including all instantons through BPS rays, including explicit twistor lines, transition functions, and a computable contact potential. It reveals an exactly solvable, mutually local sector and establishes compatibility with symplectic invariance and the wall-crossing structure encoded by Donaldson-Thomas invariants. Overall, the work furnishes a practical, geometrically driven method to compute HM metrics with complete D2-instanton corrections and clarifies the role of twistor geometry in nonperturbative string constructions.

Abstract

We present some results on instanton corrections to the hypermultiplet moduli space in Calabi-Yau compactifications of Type II string theories. Previously, using twistor methods, only a class of D-instantons (D2-instantons wrapping A-cycles) was incorporated exactly and the rest was treated only linearly. We go beyond the linear approximation and give a set of holomorphic functions which, through a known procedure, capture the effect of D-instantons at all orders. Moreover, we show that for a sector where all instanton charges have vanishing symplectic invariant scalar product, the hypermultiplet metric can be computed explicitly.