KT and HKT Geometries in Strings and in Black Hole Moduli Spaces

Some selected applications of KT and HKT geometries in string theory, supergravity, black hole moduli spaces and hermitian geometry are reviewed. It is shown that the moduli spaces of a large class of five-dimensional supersymmetric black holes are HKT spaces. In hermitian geometry, it is shown that a compact, conformally balanced, strong KT manifold whose associated KT connection has holonomy contained in SU(n) is Calabi-Yau. The implication of this result in the context of some string compactifications is explained.Comment: 26 pages, Contribution to the Proceedings of the Bonn workshop on "Special Geometric Structures in String Theory", a change in terminology and some other minor change

New potentials for conformal mechanics

We find under some mild assumptions that the most general potential of 1-dimensional conformal systems with time independent couplings is expressed as $V=V_0+V_1$, where $V_0$ is a homogeneous function with respect to a homothetic motion in configuration space and $V_1$ is determined from an equation with source a homothetic potential. Such systems admit at most an SL(2,\bR) conformal symmetry which, depending on the couplings, is embedded in Diff(R)$in three different ways. In one case,$SL(2,\bR)$is also embedded in Diff(S^1). Examples of such models include those with potential$V=\alpha x^2+\beta x^{-2}$for arbitrary couplings$\alpha$and$\beta$, the Calogero models with harmonic oscillator couplings and non-linear models with suitable metrics and potentials. In addition, we give the conditions on the couplings for a class of gauge theories to admit a$SL(2,\bR)$conformal symmetry. We present examples of such systems with general gauge groups and global symmetries that include the isometries of$AdS_2 x S^3$and$AdS_2 x S^3 x S^3$which arise as backgrounds in$AdS_2/CFT_1$.Comment: 15 pages, significant changes, references adde

Seeking the balance: Patching double and exceptional field theories

We investigate the patching of double and exceptional field theories. In double field theory the patching conditions imposed on the spacetime after solving the strong section condition imply that the 3-form field strength $H$ is exact. A similar conclusion can be reached for the form field strengths of exceptional field theories after some plausive assumptions are made on the relation between the transition functions of the additional coordinates and the patching data of the form field strengths. We illustrate the issues that arise, and explore several alternative options which include the introduction of C-folds and of the topological geometrisation condition.Comment: substantial changes, section with example added, to appear in jhep, 24 page

Brane Surgery with Thom Classes

We propose a method to investigate the conservation of brane charges at the intersection of two or more branes using the Thom classes of their normal bundles. In particular we find a relation between the charge of the branes involved in the configuration and the charge of the defects on the branes due to the intersection. We also explore the applications of our method for various brane intersections in type II strings and M-theory.Comment: 20 pages, Phyzz

The Universality of M-branes

We review the evidence for the various dualities amongst the five D=10 superstring theories and for the existence of M-theory using the associated effective supergravity theories. We also summarise the combinatorial technics developed for constructing BPS solutions in D=11 supergravity theory and conjecture that all the BPS solutions of D<11 supergravity theories can be derived from the BPS solutions of D=11 supergravity that preserve 1/2 the supersymmetry. To demonstrate this, we derive the dyonic p-brane solutions from eleven dimensions.Comment: Many changes have been made in the text and some references have been added. 8 pages, Latex, Talk at the Imperial College Workshop 5-10 Jul

Grassmannians,Calibrations and Five-Brane Intersections

We present a geometric construction of a new class of hyper-Kahler manifolds with torsion. This involves the superposition of the four-dimensional hyper-Kahler geometry with torsion associated with the NS-5-brane along quaternionic planes in quaternionic k-space, \bH^k. We find the moduli space of these geometries and show that it can be constructed using the bundle space of the canonical quaternionic line bundle over a quaternionic projective space. We also investigate several special cases which are associated with certain classes of quaternionic planes in \bH^k. We then show that the eight-dimensional geometries we have found can be constructed using quaternionic calibrations. We generalize our construction to superpose the same four-dimensional hyper-Kahler geometry with torsion along complex planes in \bC^{2k}. We find that the resulting geometry is Kahler with torsion. The moduli space of these geometries is also investigated. In addition, the applications of these new geometries to M-theory and sigma models are presented. In particular, we find new solutions of IIA supergravity with the interpretation of intersecting NS-5-branes at Sp(2)-angles on a string and show that they preserve 3/32, 1/8, 5/32 and 3/16 of supersymmetry. We also show that two-dimensional sigma models with target spaces the above manifolds have (p,q) extended supersymmetry.Comment: 39 pages, phyzzx; a previously undetermined fraction of supersymmetry has now been fixed; a table has been replaced; version submitted for publication in CM