Article

# Supergravity description of spacetime instantons

Classical and Quantum Gravity (Impact Factor: 3.56). 08/2006; DOI: 10.1088/0264-9381/24/3/001

Source: arXiv

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**ABSTRACT:**We study a class of supersymmetric spinning particle models derived from the radial quantization of stationary, spherically symmetric black holes of four dimensional [TEX equation: {{\mathcal N} = 2}] supergravities. By virtue of the c-map, these spinning particles move in quaternionic Kähler manifolds. Their spinning degrees of freedom describe mini-superspace-reduced supergravity fermions. We quantize these models using BRST detour complex technology. The construction of a nilpotent BRST charge is achieved by using local (worldline) supersymmetry ghosts to generate special holonomy transformations. (An interesting byproduct of the construction is a novel Dirac operator on the superghost extended Hilbert space.) The resulting quantized models are gauge invariant field theories with fields equaling sections of special quaternionic vector bundles. They underly and generalize the quaternionic version of Dolbeault cohomology discovered by Baston. In fact, Baston’s complex is related to the BPS sector of the models we write down. Our results rely on a calculus of operators on quaternionic Kähler manifolds that follows from BRST machinery, and although directly motivated by black hole physics, can be broadly applied to any model relying on quaternionic geometry.Communications in Mathematical Physics 01/2011; 302(3). · 1.97 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**We study the symmetries of pure = 2 supergravity in D = 4. As is known, this theory reduced on one Killing vector is characterised by a non-linearly realised symmetry SU(2,1) which is a non-split real form of SL(3,). We consider the BPS brane solutions of the theory preserving half of the supersymmetry and the action of SU(2,1) on them. Furthermore we provide evidence that the theory exhibits an underlying algebraic structure described by the Lorentzian Kac-Moody group SU(2,1)+++. This evidence arises both from the correspondence between the bosonic space-time fields of = 2 supergravity in D = 4 and a one-parameter sigma-model based on the hyperbolic group SU(2,1)++, as well as from the fact that the structure of BPS brane solutions is neatly encoded in SU(2,1)+++. As a nice by-product of our analysis, we obtain a regular embedding of the Kac-Moody algebra (2,1)+++ in 11 based on brane physics.Journal of High Energy Physics 08/2009; 2009(08):098. · 5.62 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**We investigate quantum corrections to the hypermultiplet moduli space M \mathcal{M} in Calabi-Yau compactifications of type II string theories, with particular emphasis on instanton effects from Euclidean NS5-branes. Based on the consistency of D- and NS5-instanton corrections, we determine the topology of the hypermultiplet moduli space at fixed string coupling, as previewed in [1]. On the type IIB side, we compute corrections from (p, k)-fivebrane instantons to the metric on M \mathcal{M} (specifically, the correction to the complex contact structure on its twistor space Z \mathcal{Z} ) by applying S-duality to the D-instanton sum. For fixed fivebrane charge k, the corrections can be written as a non-Gaussian theta series, whose summand for k = 1 reduces to the topological A-model amplitude. By mirror symmetry, instanton corrections induced from the chiral type IIA NS5-brane are similarly governed by the wave function of the topological B-model. In the course of this investigation we clarify charge quantization for coherent sheaves and find hitherto unnoticed corrections to the Heisenberg, monodromy and S-duality actions on M \mathcal{M} , as well as to the mirror map for Ramond-Ramond fields and D-brane charges. KeywordsNonperturbative Effects–Discrete and Finite Symmetries–Topological Strings–String DualityJournal of High Energy Physics 2011(3):1-74. · 5.62 Impact Factor

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