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The Kerr/CFT correspondence is the conjectured holographic duality between Kerr black holes and a two dimensional conformal field theory. The original conjecture applies for four dimensional extremal Kerr, but later there are various generalizations in many directions. In this talk, I will first review how Kerr/CFT works for extremal, near-extremal and non-extremal Kerr black holes. Then I will describe some recent developments on the microscopic understanding of Kerr/CFT by studying some five dimensional examples.

Starting with type IIB string theory compactified on an orientifold of a Swiss-Cheese Calabi-Yau expressed as a degree-18 hypersurface in the weighted complex projective space WCP4(1,1,1,6,9), in the presence of a mobile space-time filling D3-brane and fluxed (stack(s) of) space-time filling D7-brane(s) wrapping the 'big' (as opposed to the 'small') divisor, we give a geometric proposal for obtaining a super-massive gravitino in the inflationary epoch and a 'light' gravitino in the present era in a single setup. We also show that the setup naturally realizes a 'mu-split supersymmetry scenario' wherein having restricted the mobile D3-brane to the big divisor, one obtains super-massive D3-brane positon moduli - identified as the two Higgs doublets - at the string scale and after 1-loop Nath-Arnowitt RG-evolution to the EW scale, one obtains one light and one super-massive Higgs doublet. Also, the fermions (quarks-leptons) corresponding to the fermionic super-partners of the Wilson line moduli, are very light but the Higgsino mass parameter is very large. I also discuss issues like neutrino masses, gluino and proton decays. As a bonus, I will discuss obtaining the geometric Kaehler potential (relevant to the moduli space Kaehler potential in the presence of a mobile D3-brane) corresponding to a Ricci-flat metric for the Swiss-Cheese Calabi-Yau used in the large volume limit using Gauged Linear Sigma Model techniques for obtaining the geometric Kaehler potential for the big divisor, and the Donaldson's algorithm for obtaining Ricci-flat metrics, as guides.

We compute three-point functions of single trace operators in planar N = 4 SYM. We consider the limit where one of the operators is much smaller than the other two. We find a precise match between weak and strong coupling in the Frolov-Tseytlin classical limit for a very general class of classical solutions. To achieve this match we clarify the issue of back-reaction and identify precisely which three-point functions are captured by a classical computation.

I will review weak-weak dualities relating scattering amplitudes to Wilson loops on the one hand and correlation functions of gauge invariant operators on the other. The Wilson loop / amplitude duality has lead to both numerical and analytic results for MHV scattering amplitudes at two-loops and beyond, including the determination of two loop MHV n-point scattering amplitudes for any n in a certain kinematical regime. The duality with correlation functions has been extended to all scattering amplitudes in the theory and we give explicit examples illustrating this.

A review of the first lessons that are emerging from the data collected so far, as seen from the point of view of a phenomenologist interested in the validation of the available theoretical tools, as preparation for the challenge of major discoveries.

I will explain how refined topological string partition functions in the Nekrasov-Shatashvilli limit naturally follow from probing the underlying quantum geometry.

Holographic superconductors are gravitational backgrounds, in the sense of gauge-gravity duality, that produce the symmetry breaking pattern and associated phenomenology of superconductors in the boundary theory dual to the gravity solution. In this talk I will describe how such systems are constructed, how they can be embedded into M-theory (and string theory) and how their hydrodynamic description at strong coupling can be derived from the gravity picture.

Recently, considerable progress has been achieved in using gauge/gravity duality for describing strongly coupled systems of relevance for condensed matter physics. In this context, I discuss both top-down approaches and bottom-up approaches to holographic superconductors where the order parameter has p-wave symmetry. In the top-down approach considered, the holographic superconductors are realized in a probe brane construction involving a probe of two D-branes at finite isospin density. The dual field theory is known explicitly. We obtain the thermodynamics, the transport properties and the Fermi surface for these systems. Moreover, we consider bottom-up approaches for p-wave superconductors in which we study the back-reaction of the required SU(2) gauge field on the geometry. We find the phase diagram. A particularly interesting feature of this model is that the shear viscosity over entropy ratio displays non-universal behaviour, it is temperature-dependent at leading order in N and lambda

Gauged supergravities arise from consistent truncations of string theory and provide a solid framework for condensed matter applications, in a context where the dual field theory is well understood. In this talk we shall discuss different models, including p-wave superconductivity by condensation of a two-form potential.

There will be three introductory 45 minute talks on non string theory approaches to quantum gravity.

Scattering amplitudes in N=4 super Yang-Mills theory have been extensively studied in recent years, due to their remarkable features. In particular, planar amplitudes exhibit a hidden symmetry, the dual superconformal symmetry. I will review how, together with the standard superconformal one, it forms a Yangian structure. Then I will discuss some recent results about the Yangian symmetry of light-like Wilson loops at one loop.

I will present an ADHMN-like construction which generates self-dual string solutions to the effective M5-brane worldvolume theory from solutions to the Basu-Harvey equation.

Some of the perturbative vacua of open string theory are known to be unstable. They decay to other (meta-)stable vacua. We will consider the dynamics of this relaxation process (decay). In particular, the equation that describes an inhomogeneous decay turns out to be a variant of a non-linear partial differential equation that appears in many other areas. We will point out their similarities and differences.

Supersymmetric invariants, their symmetries and various approaches to contructing them are discussed. Their role in investigating the onset of UV divergences is outlined. In particular, it is argued that D=4 N=8 supergravity is finite up to, and including, 6 loops.