Among the very first examples of hyper-Kahler manifolds given by Calabi in 1979, there were the cotangent bundles of complex projective spaces, T-star-CPn. Later on, many more examples of hyper-Kahler metrics on cotangent bundles of Kahler manifolds were shown to exist. Finally, Kaledin (1997) and Feix (1999) proved that a real-analytic Kahler metric on a complex manifold M can always be extended to a hyper-Kahler metric in a neighborhood of M in T-star-M. Although these mathematical proofs are rather technical and involved, there exists a streamlined physical construction which leads to the same results and is based on the concept of supersymmetry. As is well-known, four- and five-dimensional N = 2 supersymmetric nonlinear sigma-models possess the property that their target spaces are hyper-Kahler manifolds. The physical construction consists of providing a manifestly N = 2 supersymmetric nonlinear sigma-model whose target space can be shown to be (a neighborhood of the zero section in) the cotangent bundle T-star-M of a Kahler manifold M. This talk will review the salient properties of such supersymmetric nonlinear sigma-models with eight supercharges.

The application of the AdS/CFT correspondence in the calculation of four point functions for chiral primary operators in the large N limit for maximal superconformal gauge theories is reviewed. It is shown how the results satisfy certain constraints, motivated by our understanding from string theory of the spectrum of operators in the large N limit, which allow a construction of the four point function for any half BPS chiral primary operator at large N.

D-branes are considered by the general particle physics community as the arcane inventions of the initiated having no relevance to even semi-realistic QFTs. In this seminar I want to provide compelling evidence that the domain walls of the simplest supersymmetric extension of QCD are D-branes for the confining string of the theory. Conventional D-brane technology then leads to a very intriguing result for the forces between the domain walls which suggests some underlying but unknown magic is at work. (based on hep-th/0505213,0601150)

In the context of integrability in AdS/CFT correspondence, we construct the Green-Schwarz-Metsaev-Tseytlin supersting in the S(5) x R(1) sector, from a set of physical particles on a circle in the integrable 1+1D sigma-model with Zamolodchikov's S-matrix. We reproduce, in the limit of high density of the particles, all finite gap KMMZ solutions for classical strings and the quantum AFS string Bethe ansatz equations, as an approximation to our construction.

I will discuss the construction supergravity plus branes solutions dual to 4d N=1 SQCD with a quartic superpotential. The geometries depend on the ratio Nf/Nc which is kept of order one. I will show how some field theory features like R-symmetry breaking, Seiberg duality, Wilson loops and pair creation, running of couplings and domain walls are encoded in the solutions.

I will describe a new formulation of Witten's open bosonic string field theory based on non-standard world-sheet parametrization. The theory dramatically simplifies and the long-searched-for tachyon vacuum can be explicitly constructed. This allows us to find a proof for one of the Sen's conjectures relating the energy of the tachyon solution to the tension of the D25-brane.

We consider classical strings propagating in a background generated by a sequence of TsT transformations. We describe a general procedure to derive the Green-Schwarz action for strings. We show that the U(1) isometry variables of the TsT-transformed background are related to the isometry variables of the initial background in a universal way independent of the details of the background. This allows us to prove that strings in the TsT-transformed background are described by the Green-Schwarz action for strings in the initial background subject to twisted boundary conditions. Our construction implies that a TsT transformation preserves integrability properties of the string sigma model. We discuss in detail type IIB strings propagating in the TsT-transformed AdS(5) x S(5) space-time and find the twisted boundary conditions for bosons and fermions. We also discuss string zero modes whose dynamics is governed by a fermionic generalization of the integrable Neumann model.

In the first part of the talk we discuss how to construct geometries sourced by branes carrying general condensates. As an example we consider fundamental strings carring fermion bilinear condensates. Dualizing to the D1-D5 system these correspond to the missing geometries needed to account for all black hole microstates in the fuzzball conjecture. In the second half of the talk we discuss new results in extracting field theory data from (asymptotically AdS) geometries. These methods can be used to show that the D1-D5 geometries do indeed correspond to R vacua with all the requisite properties.

We investigate quaternionic (especially hyperkahler) analogues of the symplectic cut construction. In low dimensions this can be interpreted as a adding a brane to a hyperkahler manifold.

Meeting of the IoP Mathematical and Theoretical Physics Group, to be held at Imperial College on the 10th and 11th of March. Registration requested. Details can be found here: http://groups.iop.org/MP/perspectives.html

I will review the recent developments in topological membrane theory. In particular I will discuss the formulation of topological membrane theory on G2-manifolds and its role in the topological M-theory. The reduction to topological strings will be presented.