C.M. Hull

Unity of superstring dualities

Abstract The effective action for type II string theory compactified on a six-torus is N = 8 supergravity, which is known to have an E7 duality symmetry. We show that this is broken by quantum effects to a discrete subgroup, E 7 ( Z ) , which contains both the T-duality group O(6, 6; Z ) and the S-duality group SL(2; Z ). We present evidence for the conjecture that E 7 ( Z ) is an exact ‘U-duality’ symmetry of type II string theory. This conjecture requires certain extreme black hole states to be identified with massive modes of the fundamental string. The gauge bosons from the Ramond-Ramond sector couple not to string excitations but to solitons. We discuss similar issues in the context of toroidal string compactifications to other dimensions, compactifications of the type II string on K3 × T2 and compactifications of 11-dimensional supermembrane theory.

A New maximally supersymmetric background of IIB superstring theory

We present a maximally supersymmetric IIB string background. The geometry is that of a conformally flat lorentzian symmetric space G/K with solvable G, with a homogeneous five-form flux. We give the explicit supergravity solution, compute the isometries, the 32 Killing spinors, and the symmetry superalgebra, and then discuss T-duality and the relation to M-theory.

All supersymmetric solutions of minimal supergravity in five dimensions

All purely bosonic supersymmetric solutions of minimal supergravity in five dimensions are classified. The solutions preserve either one half or all of the supersymmetry. Explicit examples of new solutions are given, including a large family of plane-fronted waves and a maximally supersymmetric analogue of the Godel universe which lifts to a solution of 11-dimensional supergravity that preserves 20 supersymmetries.

Penrose limits and maximal supersymmetry

We show that the maximally supersymmetric pp-wave of IIB superstring and M-theories can be obtained as a Penrose limit of the supersymmetric AdS × S solutions. In addition, we find that in a certain large tension limit, the geometry seen by a brane probe in an AdS × S background is either Minkowski space or a maximally supersymmetric pp-wave.

Duality in the type-II superstring effective action

Abstract We derive the T -duality transformations that transform a general d = 10 solution of the type-IIA string with one isometry to a solution of the type-IIB string with one isometry and vice versa. In contrast to other superstring theories, the T -duality transformations are not related to a non-compact symmetry of a d = 9 supergravity theory. We also discuss S -duality in d = 9 and d = 10 and the relationship with eleven-dimensional supergravity theory. We apply these dualities to generate new solutions of the type-11A and type-IIB superstrings and of eleven-dimensional supergravity.

Generalized metric formulation of double field theory

The generalized metric is a T-duality covariant symmetric matrix constructed from the metric and two-form gauge field and arises in generalized geometry. We view it here as a metric on the doubled spacetime and use it to give a simple formulation with manifest T-duality of the double field theory that describes the massless sector of closed strings. The gauge transformations are written in terms of a generalized Lie derivative whose commutator algebra is defined by a double field theory extension of the Courant bracket.

Background independent action for double field theory

Double field theory describes a massless subsector of closed string theory with both momentum and winding excitations. The gauge algebra is governed by the Courant bracket in certain subsectors of this double field theory. We construct the associated nonlinear background-independent action that is T-duality invariant and realizes the Courant gauge algebra. The action is the sum of a standard action for gravity, antisymmetric tensor, and dilaton fields written with ordinary derivatives, a similar action for dual fields with dual derivatives, and a mixed term that is needed for gauge invariance.

Timelike T-duality, de Sitter space, large N gauge theories and topological field theory

T-Duality on a timelike circle does not interchange IIA and IIB string theories, but takes the IIA theory to a type IIB* theory and the IIB theory to a type IIA* theory. The type II* theories admit E-branes, which are the images of the type II D-branes under timelike T-duality and correspond to imposing Dirichlet boundary conditions in time as well as some of the spatial directions. The effective action describing an En-brane is the n-dimensional Euclidean super-Yang-Mills theory obtained by dimensionally reducing 9+1 dimensional super-Yang-Mills on 9−n spatial dimensions and one time dimension. The IIB* theory has a solution which is the product of 5-dimensional de Sitter space and a 5-hyperboloid, and the E4-brane corresponds to a non-singular complete solution which interpolates between this solution and flat space. This leads to a duality between the large N limit of the Euclidean 4-dimensional U(N) super-Yang-Mills theory and the IIB* string theory in de Sitter space, and both are invariant under the same de Sitter supergroup. This theory can be twisted to obtain a large N topological gauge theory and its topological string theory dual. Flat space-time appears to be an unstable vacuum for the type II* theories, but they have supersymmetric cosmological solutions.

Doubled geometry and T-folds

The doubled formulation of string theory, which is T-duality covariant and enlarges spacetime with extra coordinates conjugate to winding number, is reformulated and its geometric and topological features examined. It is used to formulate string theory in T-fold backgrounds with T-duality transition functions and a quantum implementation of the constraints of the doubled formalism is presented. This establishes the quantum equivalence to the usual sigma-model formalism for world-sheets of arbitrary genus, provided a topological term is added to the action. The quantisation involves a local choice of polarisation, but the results are independent of this. The natural dilaton of the doubled formalism is duality-invariant and so T-duality is a perturbative symmetry for the perturbation theory in the corresponding coupling constant. It is shown how this dilaton is related to the dilaton of the conventional sigma-model which does transform under T-duality. The generalisation of the doubled formalism to the superstring is given and shown to be equivalent to the usual formulation. Finally, the formalism is generalised to one in which the whole spacetime is doubled.

Generalised geometry for M-theory

Generalised geometry studies structures on a d-dimensional manifold with a metric and 2-form gauge field on which there is a natural action of the group SO(d, d). This is generalised to d-dimensional manifolds with a metric and 3-form gauge field on which there is a natural action of the group Ed. This provides a framework for the discussion of M-theory solutions with flux. A different generalisation is to d-dimensional manifolds with a metric, 2-form gauge field and a set of p-forms for p either odd or even on which there is a natural action of the group Ed+1. This is useful for type IIA or IIB string solutions with flux. Further generalisations give extended tangent bundles and extended spin bundles relevant for non-geometric backgrounds. Special structures that arise for supersymmetric backgrounds are discussed.