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...

We point out that SO(2N(c)) gauge theory with N(f) fundamental Dirac fermions does not have a sign problem at finite baryon number chemical potential μ(B). One can thus use lattice Monte Carlo simulations to study this theory at finite density. The absence of a sign problem in the SO(2N(c)) theory is particularly interesting because a wide class of observables in the SO(2N(c)) theory coincide with observables in QCD in the large N(c) limit, as we show using the technique of large N(c) orbifold equivalence. We argue that the orbifold equivalence between the two theories continues to hold at finite μ(B) provided one adds appropriate deformation terms to the SO(2N(c)) theory. This opens up the prospect of learning about QCD at finite μ(B) using lattice studies of the SO(2N(c)) theory.

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.

In a recent paper, Witten proposed a surprising connection between perturbative gauge theory and a certain topological model in twistor space. In particular, he showed that gluon amplitudes are localized on holomorphic curves. In this note we present some preliminary considerations on the possibility of having a similar localization for gravity amplitudes.