Massive (perturbative) string states are interesting in many respects (cosmology, black hole Physics, production at accelerators). We review the research done in order to find the perturbative massive superstring states with very long lifetime, the characteristics of their decay, the emission spectrum, both in fully extended space-time and in the case of toroidal compactifications. The main result is the identification of a particular state with very long lifetime decaying only by gravitational emission and with thermal-like spectrum.

I will discuss the newly discovered Y(p,q) quiver gauge theories, which are dual to Type IIB string theory on AdS5 x Y(p,q). The metrics on the five-dimensional Y(p,q) manifolds are explicitly known, thus opening up exciting possibilities. Special emphasis will be placed on the toric phases of these theories and their Seiberg duality structure.

We consider the heterotic string on certain six-dimensional half-flat manifolds which arise in the context of mirror symmetry. The four-dimensional N=1 effective theory is derived including the superpotential induced by the intrinsic torsion and NS NS flux. From the calculation of the gravitino mass term, we also obtain a general Gukov type formula valid for all heterotic compactifications on manifolds with SU(3) structure. The results are used to study heterotic AdS4 vacua which arise from the flux superpotential combined with gaugino condensation.

I will give an introduction to the novel method of calculating scattering amplitudes in gauge theory with twistor-space string theory inspired rules. I will show how the method works in simple cases and discuss recent new results for the amplitudes obtained at tree and loop level. I'll discuss some known puzzles, the ways to resolve them, open questions and future directions, including issues in string theory, quantum field theory and phenomenology.

This talk is part of the joint Triangular Seminars.

Using the example of WZW D-branes, I will explain how loop operators, corresponding to bulk conformal defects, generate new consistent D-branes from old ones. I will comment on possible extensions to more general geometries.

We will generalize the concept of partial and complete observables, intruduced by Rovelli, to constrained systems with an arbitrary number of (first class) constraints and to canonical field theories. Different methods to calculate complete observables (aka Dirac observables) will be presented and applied to examples, moreover their algebraic properties will be considered. Furthermore we will investigate whether it is possible to calculate complete observables in stages. In the case of gravity this will answer the question , whether it is possible to calculate the complete observable with respect to the Hamiltonian constraints, starting from 3-diffeomorphism invariant partial observables.

In the supergravity approximation of the AdS/CFT correspondence correlation fucntions of the strongly coupled gauge theory can be computed by evaluating the on-shell supergravity action with arbitrary Dirichlet boundary conditions for the various fields. It is well known, however, that the on-shell action on the conformal boundary of AdS diverges due to the infinite volume of the bulk. Holographic Renormalization is a method for systematically constructing covariant counter terms which remove the divergences of the on-shell supergravity action for any asymptotically AdS space and it provides an algorithm for calculating renormalized correlation functions of the strongly coupled gauge theory. I will review the main steps involved in this algorithm and present a recently developed Hamiltonian version of the method where the AdS radius plays the role of time in the Hamiltonian formalism. I will then apply this method to calculate correlation functions in the field theory duals of various Poincare and AdS-sliced domain wall solutions of five dimensional gauged supergravity, including the recently discovered Janus background.

Witten's twistor string theory description of N=4 super Yang-Mills has led to much progress in perturbative Yang-Mills theory this year, with accumulating evidence for the localisation of scattering amplitudes in twistor space in various Yang-Mills theories. This talk will focus on the MHV diagram approach, which builds in localisation, and will describe work done at Queen Mary which shows how to define MHV diagrams at loop level. This has been successfully applied to give the general one-loop MHV amplitudes in N=4 and N=1 super Yang-Mills.

Generalised black holes have a horizon given by an arbitrary Einstein manifold. I will describe a criterion for the classical stability of these black holes. Roughly, spherical horizons are stable but lemon-shaped horizons can be unstable. In Anti-de Sitter space, these black holes are dual to gauge theory on a curved background given by the same Einstein manifold. I will argue that the dual thermal field theory effect is a novel phase transition induced by inhomogeneous Casimir pressures and characterised by a condensation of pressure.

In the last year and a half, many new tests of the AdS/CFT correspondence have been achieved by studying a certain class of non-topological solitons corresponding to rotating strings which carry (at least) two large angular momenta. They are dual to CFT operators which are far away from the 1/2 BPS operators of Berenstein, Maldacena and Nastase. We will discuss to which point can these results test the AdS/CFT away from supersymmetry.

I will summarise recent progress in understanding the dynamics of vortices in gauge theories and describe how the vortices can be used as probes to extract information about the strong coupling quantum dynamics of the theory in which its embedded.

This is part of the London topology and geometry seminars