Stefan Vandoren

D-instantons and twistors

Finding the exact, quantum corrected metric on the hypermultiplet moduli space in Type II string compactifications on Calabi-Yau threefolds still poses an outstanding open problem. We address this issue by relating the quaternionic-Kahler metric on the hypermultiplet moduli space to the complex contact geometry on its twistor space. In this framework, Euclidean D-brane instanton contributions are captured by contact transformations between different locally flat patches. We derive those by recasting the previously known A-type D2-instanton corrections in the language of contact geometry, covariantizing the result under electro-magnetic duality, and using mirror symmetry. As a result, we are able to express the effects of all D-instantons in Type II compactifications concisely as a sum of dilogarithm functions. We conclude with some comments on the relation to microscopic degeneracies of four-dimensional BPS black holes and to the wall-crossing formula of Kontsevich and Soibelman, and on the form of the yet unknown NS5-brane instanton contributions.

N=2 supergravity in five dimensions revisited

We construct matter-coupled N = 2 supergravity in five dimensions, using the superconformal approach. For the matter sector we take an arbitrary number of vector, tensor and hypermultiplets. By allowing off-diagonal vector-tensor couplings we find more general results than currently known in the literature. Our results provide the appropriate starting point for a systematic search for BPS solutions, and for applications of M-theory compactifications on Calabi-Yau manifolds with fluxes.

Multi-instanton calculus and the AdS / CFT correspondence in N=4 superconformal field theory

Abstract We present a self-contained study of ADHM multi-instantons in SU(N) gauge theory, especially the novel interplay with supersymmetry and the large-N limit. We give both field- and string-theoretic derivations of the N = 4 supersymmetric multi-instanton action and collective coordinate integration measure. As a central application, we focus on certain n-point functions Gn, n = 16, 8 or 4, in N = 4 SU(N) gauge theory at the conformal point (as well as on related higher-partial-wave correlators); these are correlators in which the 16 exact supersymmetric and superconformal fermion zero-modes are saturated. In the large-N limit, for the first time in any four-dimensional theory, we are able to evaluate all leading-order multi-instanton contributions exactly. We find compelling evidence for Maldacenas conjecture: (1) The large = N k-instanton collective coordinate space has the geometry of a single copy of AdS5 × S5. (2) The integration measure on this space includes the partition function of ten-dimensional N = 1 SU(k) gauge theory dimensionally reduced to zero dimensions, matching the description of D-instantons in Type IIB string theory. (3) In exact agreement with Type IIB string calculations, at the k-instantonlevel, G n = √N g 8 k n− 7 2 e 2πikτ Σ d/k d −2 · F n (x 1 , …, x n ) , where Fn is identical to a convolution of n bulk-to-boundary supergravity propagators.

Black holes and black branes in Lifshitz spacetimes

We construct analytic solutions describing black holes and black branes in asymptotically Lifshitz spacetimes with arbitrary dynamical exponent z and for arbitrary number of dimensions. The model considered consists of Einstein gravity with negative cosmological constant, a scalar, and N U(1) gauge fields with dilatonic-like couplings. We study the phase diagrams and thermodynamic instabilities of the solution, and find qualitative differences between the cases with 1 ≤ z < 2, z = 2 and z > 2.

String loop corrected hypermultiplet moduli spaces

Using constraints from supersymmetry and string perturbation theory, we determine the string loop corrections to the hypermultiplet moduli space of type II strings compactified on a generic Calabi-Yau threefold. The corresponding quaternion-Kahler manifolds are completely encoded in terms of a single function. The latter receives a one-loop correction and, using superspace techniques, we argue for the existence of a non-renormalization theorem excluding higher loop contributions.

Superconformal N = 2, D = 5 matter with and without actions

We investigate N = 2, D = 5 supersymmetry and matter-coupled supergravity theories in a superconformal context. In a first stage we do not require the existence of a lagrangian. Under this assumption, we already find at the level of rigid supersymmetry, i.e. before coupling to conformal supergravity, more general matter couplings than have been considered in the literature. For instance, we construct new vector-tensor multiplet couplings, theories with an odd number of tensor multiplets, and hypermultiplets whose scalar manifold geometry is not hyperkahler. Next, we construct rigid superconformal lagrangians. This requires some extra ingredients that are not available for all dynamical systems. However, for the generalizations with tensor multiplets mentioned above, we find corresponding new actions and scalar potentials. Finally, we extend the supersymmetry to local superconformal symmetry, making use of the Weyl multiplet. Throughout the paper, we will indicate the various geometrical concepts that arise, and as an application we compute the non-vanishing components of the Ricci tensor of hypercomplex group manifolds. Our results can be used as a starting point to obtain more general matter-couplings to Poincare supergravity.

Static supersymmetric black holes in AdS4 with spherical symmetry

We elaborate further on the static supersymmetric AdS4 black holes found in [1], investigating thoroughly the BPS constraints for spherical symmetry in N = 2 gauged supergravity in the presence of Fayet-Iliopoulos terms. We find Killing spinors that preserve two of the original eight supercharges and investigate the conditions for genuine black holes free of naked singularities. The existence of a horizon is intimately related with the requirement that the scalars are not constant, but given in terms of harmonic functions in analogy to the attractor flow in ungauged supergravity. The black hole charges depend on the choice of the electromagnetic gauging, with only magnetic charges for purely electric gaugings. Finally we show how these black holes can be embedded in N = 8 supergravity and thus in M-theory.

Nonperturbative corrections to 4D string theory effective actions from SL(2,Z) duality and supersymmetry

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 world sheet instanton corrections into a single modular invariant function that determines the hypermultiplet low-energy effective action.

Hypermultiplets and topological strings

The c-map relates classical hypermultiplet moduli spaces in compactifications of type II strings on a Calabi-Yau threefold to vector multiplet moduli spaces via a further compactification on a circle. We give an off-shell description of the c-map in N = 2 superspace. The superspace Lagrangian for the hypermultiplets is a single function directly related to the prepotential of special geometry, and can therefore be computed using topological string theory. Similarly, a class of higher derivative terms for hypermultiplets can be computed from the higher genus topological string amplitudes. Our results provide a framework for studying quantum corrections to the hypermultiplet moduli space, as well as for understanding the black hole wave-function as a function of the hypermultiplet moduli.

Instantons, three-dimensional gauge theory, and the Atiyah-Hitchin manifold

Abstract We investigate quantum effects on the Coulomb branch of three-dimensional N = 4 super-symmetric gauge theory with gauge group SU (2). We calculate perturbative and one-instanton contributions to the Wilsonian effective action using standard weak-coupling methods. Unlike the four-dimensional case, and despite supersymmetry, the contribution of non-zero-modes to the instanton measure does not cancel. Our results allow us to fix the weak-coupling boundary conditions for the differential equations which determine the hyper-Kahler metric on the quantum moduli space. We confirm the proposal of Seiberg and Witten that the Coulomb branch is equivalent, as a hyper-Kahler manifold, to the centered moduli space of two BPS monopoles constructed by Atiyah and Hitchin.