I will provide a brief general introduction into non-Hermitian Hamiltonian systems with real eigenvalue spectra, arguing that they represent well defined self consistent physical systems. Such type of models possess usually an antilinear symmetry, as for instance PT-invariance (simultaneous parity and time reversal) and/or are quasi/pseudo Hermitian. Most crucial is that they allow for a consistent quantum mechanical framework possessing a unitary time evolution. The general framework will be applied to some integrable models, such a quantum spin chains, classical integrable systems associated to differential equations and Calogero-Moser-Sutherland models. I will present some recent results.

In this talk we will briefly review the recent progress in the semiclassical string theory calculation of non-BPS gauge theory three-point correlation functions at strong coupling. We will then discuss the light-cone path integral approach to such three-point functions with a focus on near-BMN operators where one can systematically go beyond the semiclassical approximation.

In my talk I will describe a class of gravitational solutions which, in the context of AdS/CFT, are dual to boundary field theories with spontaneous symmetry breaking and thus give rise to a superfluid phase. I will give a general introduction to the ideas of quantum criticality and how AdS/CFT techniques may be applied to such systems. I will then use the tools of gauge/gravity duality to demonstrate that the boundary description of such systems, in the hydrodynamical limit, is governed by a relativistic generalisation of the Tisza-Landau two-fluid model.

http://www.kcl.ac.uk/nms/depts/physics/news/TheNewPhysics AT theLHC.aspx

I will present recent progress in the understanding of two-dimensional sigma-models on the supergroup PSl(nIn). I will emphasize the relevance of these models to study quantum integrability in the AdS/CFT correspondence. In particular i will explain the computation of the fusion of some line operators, the transfer matrices, that encode an infinite number of conserved charges. This computation leads to a first-principle, perturbative derivation of the Hirota equation, which has been argued to provide a solution to the spectrum problem in N=4 SYM.

We revisit the relation of the six-dimensional (2, 0) M5-brane Conformal Field Theory compactified on a circle to 5D maximally supersymmetric Yang-Mills Gauge Theory. We show that in the broken phase 5D super-Yang-Mills contains a spectrum of soliton states that can be identified with the complete Kaluza-Klein modes of an M2-brane ending on the M5-branes. This provides evidence that the (2,0) theory on a circle is equivalent to 5D super-Yang-Mills with no additional UV degrees of freedom, suggesting that the latter is in fact a well-defined quantum theory and possibly finite.

We reformulate M-theory in a duality manifest way using generalised geometry.

I will review recent progress in understanding the 3d N=2 superconformal field theories which describe the low energy dynamics of M2-branes probing toric CY_4 cones in M-theory, based on a KK reduction of M-theory to type IIA string theory. A key role in field theory is played by 't Hooft monopole operators, disorder operators which encode the geometric details of the reduction.

After briefly reviewing the notion of geometries characterised by SU(3) structures, I will discuss a particular class known (in String Theory) as non-Kahler. I will explain how this arises both in Type II and Heterotic Supergravities. Two explicit constructions of these geometries will be discussed. One is a one-parameter solution corresponding to fivebranes wrapped on the two-sphere of the resolved conifold, that can be thought of as a non-Kahler analog of the conifold. The other is a general construction of one-parameter non-Kahler deformations of Calabi-Yau manifolds with a U(1) isometry, where the non-Abelian Yang-Mills field of the Heterotic is non-trivial. The presentation will be loosely based on the two papers: arXiv:0906.0591 and arXiv:1010.4031.

The Y-system, originating from integrability, is a tool describing the exact spectrum in 4D N=4 Super-Yang-Mills theory in a planar limit. We describe the construction and discuss predictions and tests for weak, strong and intermediate couplings.