Toric Calabi-Yau supermanifolds and mirror symmetry

We study mirror symmetry of supermanifolds constructed as fermionic extensions of compact toric varieties. We mainly discuss the case where the linear sigma A-model contains as many fermionic fields as there are U(1) factors in the gauge group. In the mirror super-Landau-Ginzburg B-model, focus is on the bosonic structure obtained after integrating out all the fermions. Our key observation is that there is a relation between the super-Calabi-Yau conditions of the A-model and quasi-homogeneity of the B-model, and that the degree of the associated superpotential in the B-model is given in terms of the determinant of the fermion charge matrix of the A-model.Comment: 20 pages, v2: references adde

On Local Calabi-Yau Supermanifolds and Their Mirrors

We use local mirror symmetry to study a class of local Calabi-Yau super-manifolds with bosonic sub-variety V_b having a vanishing first Chern class. Solving the usual super- CY condition, requiring the equality of the total U(1) gauge charges of bosons \Phi_{b} and the ghost like fields \Psi_{f} one \sum_{b}q_{b}=\sum_{f}Q_{f}, as \sum_{b}q_{b}=0 and \sum_{f}Q_{f}=0, several examples are studied and explicit results are given for local A_{r} super-geometries. A comment on purely fermionic super-CY manifolds corresponding to the special case where q_{b}=0, \forall b and \sum_{f}Q_{f}=0 is also made.\bigskipComment: 17 page

S-duality and Topological Strings

In this paper we show how S-duality of type IIB superstrings leads to an S-duality relating A and B model topological strings on the same Calabi-Yau as had been conjectured recently: D-instantons of the B-model correspond to A-model perturbative amplitudes and D-instantons of the A-model capture perturbative B-model amplitudes. Moreover this confirms the existence of new branes in the two models. As an application we explain the recent results concerning A-model topological strings on Calabi-Yau and its equivalence to the statistical mechanical model of melting crystal.Comment: 13 page

Non-supersymmetric Black Holes and Topological Strings

We study non-supersymmetric, extremal 4 dimensional black holes which arise upon compactification of type II superstrings on Calabi-Yau threefolds. We propose a generalization of the OSV conjecture for higher derivative corrections to the non-supersymmetric black hole entropy, in terms of the one parameter refinement of topological string introduced by Nekrasov. We also study the attractor mechanism for non-supersymmetric black holes and show how the inverse problem of fixing charges in terms of the attractor value of CY moduli can be explicitly solved.Comment: 47 pages, harvmac. v2: footnote(4) expanded, references adde

Matrix Models and D-branes in Twistor String Theory

We construct two matrix models from twistor string theory: one by dimensional reduction onto a rational curve and another one by introducing noncommutative coordinates on the fibres of the supertwistor space P^(3|4)->CP^1. We comment on the interpretation of our matrix models in terms of topological D-branes and relate them to a recently proposed string field theory. By extending one of the models, we can carry over all the ingredients of the super ADHM construction to a D-brane configuration in the supertwistor space P^(3|4). Eventually, we present the analogue picture for the (super) Nahm construction.Comment: 1+37 pages, reference added, JHEP style, published versio

Quantum Attractor Flows

Motivated by the interpretation of the Ooguri-Strominger-Vafa conjecture as a holographic correspondence in the mini-superspace approximation, we study the radial quantization of stationary, spherically symmetric black holes in four dimensions. A key ingredient is the classical equivalence between the radial evolution equation and geodesic motion of a fiducial particle on the moduli space M^*_3 of the three-dimensional theory after reduction along the time direction. In the case of N=2 supergravity, M^*_3 is a para-quaternionic-Kahler manifold; in this case, we show that BPS black holes correspond to a particular class of geodesics which lift holomorphically to the twistor space Z of M^*_3, and identify Z as the BPS phase space. We give a natural quantization of the BPS phase space in terms of the sheaf cohomology of Z, and compute the exact wave function of a BPS black hole with fixed electric and magnetic charges in this framework. We comment on the relation to the topological string amplitude, extensions to N>2 supergravity theories, and applications to automorphic black hole partition functions.Comment: 43 pages, 6 figures; v2: typos and references added; v3: published version, minor change

Twistor Strings with Flavour

We explore the tree-level description of a class of N=2 UV-finite SYM theories with fundamental flavour within a topological B-model twistor string framework. In particular, we identify the twistor dual of the Sp(N) gauge theory with one antisymmetric and four fundamental hypermultiplets, as well as that of the SU(N) theory with 2N hypermultiplets. This is achieved by suitably orientifolding/orbifolding the original N=4 setup of Witten and adding a certain number of new topological 'flavour'-branes at the orientifold/orbifold fixed planes to provide the fundamental matter. We further comment on the appearance of these objects in the B-model on CP(3|4). An interesting aspect of our construction is that, unlike the IIB description of these theories in terms of D3 and D7-branes, on the twistor side part of the global flavour symmetry is realised geometrically. We provide evidence for this correspondence by calculating and matching amplitudes on both sides.Comment: 38+12 pages; uses axodraw.sty. v2: References added, minor clarification

Wilson Loops, Geometric Transitions and Bubbling Calabi-Yau's

Motivated by recent developments in the AdS/CFT correspondence, we provide several alternative bulk descriptions of an arbitrary Wilson loop operator in Chern-Simons theory. Wilson loop operators in Chern-Simons theory can be given a description in terms of a configuration of branes or alternatively anti-branes in the resolved conifold geometry. The representation of the Wilson loop is encoded in the holonomy of the gauge field living on the dual brane configuration. By letting the branes undergo a new type of geometric transition, we argue that each Wilson loop operator can also be described by a bubbling Calabi-Yau geometry, whose topology encodes the representation of the Wilson loop. These Calabi-Yau manifolds provide a novel representation of knot invariants. For the unknot we confirm these identifications to all orders in the genus expansion.Comment: 26 pages; v.2 typos corrected, explanations clarified; v.3 typos corrected, reference adde