We find the D(−1) and D1-brane instanton contributions to the hypermultiplet moduli space of type IIB string compactifications on Calabi-Yau threefolds. These combine with known perturbative and worldsheet instanton corrections into a single modular invariant function that determines the hypermultiplet low-energy effective action. 04.65.+e The absence of a complete nonperturbative formulation of string theory is its main shortcoming as a fullfledged quantum theory unifying all known fundamental interactions. Empirically, perturbative weakly coupled string theory does not give a detailed description of our universe; consequently, the understanding of nonperturbative phenomena is essential to making possible a detailed confrontation of string theory and experiment. Generally, it is difficult to obtain exact information about nonperturbative structures. However, in special cases such as those presented here, the symmetries and dualities of the theory are powerful enough to fix the exact couplings in the low-energy effective action.The examples we consider are provided by type II string compactifications on Calabi-Yau threefolds (CY), where the four-dimensional effective actions are constrained by N = 2 supersymmetry. The massless fields are components of a supergravity multiplet, vector multiplets, or hypermultiplets. Their scalar fields parametrize moduli spaces M VM and M HM , respectively, which locally form a direct product [1]. The special geometry of M VM is determined by a holomorphic function F (X) [2]. The exact expression for this function includes perturbative and worldsheet instanton corrections in the inverse string tension α ′ , which can in principle be computed by mirror symmetry, see e.g. [3]. (See Fig. 1 for details.) On the other hand, the string coupling constant g s is set by the vacuum expectation value of the dilaton, whose four-dimensional reduction belongs to a hypermultiplet. Thus M HM receives both perturbative and nonperturbative g s corrections. Building on earlier work [4,5], the perturbative corrections have recently been understood in [6]. The nonperturbative corrections arise in the IIA case from Euclidean D2 or NS5-branes wrapping around supersymmetric three-cycles or the entire CY, respectively, and in the IIB case from D(−1)-instantons as well as D1, D3, D5, and NS5-branes wrapping holomorphic cycles in the CY [7]. Little is known about summing up such corrections -see however [8,9] for some results in the limit where gravity decouples.In this letter, we use the constraints from supersymmetry and the SL(2, Z) duality symmetry of IIB string theory to determine the full D(−1) and D1-brane instanton corrected low-energy effective action for hypermultiplets in type IIB compactifications on CY. This provides a large class of four-dimensional N = 2 supergravity theories where exact results are obtained to all orders in both α ′ and g s ; such results were not available in four dimensions previously.Similar ideas were applied in [10,11,12,13] to obtain instanton corrections to highe...

The double-tensor multiplet naturally appears in type IIB superstring compactifications on Calabi-Yau threefolds, and is dual to the universal hypermultiplet. We revisit the calculation of instanton corrections to the low-energy effective action, in the supergravity approximation. We derive a Bogomol'nyi bound for the double-tensor multiplet and find new instanton solutions saturating the bound. They are characterized by the topological charges and the asymptotic values of the scalar fields in the double-tensor multiplet. The double-tensor multipletAs mentioned in the introduction, we are interested in the case of a single hypermultiplet coupled to N = 2 supergravity. Classically, the four scalars of the universal hypermultiplet

We investigate membrane instanton effects in type IIA strings compactified on rigid CalabiYau manifolds. These effects contribute to the low-energy effective action of the universal hypermultiplet. In the absence of additional fivebrane instantons, the quaternionic geometry of this hypermultiplet is determined by solutions of the three-dimensional Toda equation. We construct solutions describing membrane instantons, and find perfect agreement with the string theory prediction. In the context of flux compactifications we discuss how membrane instantons contribute to the scalar potential and the stabilization of moduli. Finally, we demonstrate the existence of meta-stable de Sitter vacua.

We use mirror symmetry to determine and sum up a class of membrane instanton corrections to the hypermultiplet moduli space metric arising in Calabi-Yau threefold compactifications of type IIA strings. These corrections are mirror to the D1 and D(−1)-brane instantons on the IIB side and are given explicitly in terms of a single function in projective superspace. The corresponding four-dimensional effective action is completely fixed by the Euler number and the genus zero Gopakumar-Vafa invariants of the mirror Calabi-Yau.

We determine the general coupling of a system of scalars and antisymmetric tensors, with at most two derivatives and undeformed gauge transformations, for both rigid and local N = 2 supersymmetry in four-dimensional spacetime. Our results cover interactions of hyper, tensor and double-tensor multiplets and apply among others to Calabi-Yau threefold compactifications of Type II supergravities. As an example, we give the complete Lagrangian and supersymmetry transformation rules of the double-tensor multiplet dual to the universal hypermultiplet.