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Physics emerged from the twentieth century with two remarkably successful descriptions of nature which stand in striking contrast. Quantum mechanics describes the subatomic realm with intrinsic uncertainties and probabilities. On the other hand, Einstein's general relativity describe gravitational phenomena in an exacting geometric arena. Theoretical physicists have struggled for over fifty years trying to combine these views in a single unified framework. More recently, superstring theory has drawn a huge amount of interest as a leading contender to provide such a unification. Superstring theory is a theory of strings, branes, extra spacetime dimensions and much more. In my lecture, I will try to give a flavour for what superstring theory is all about and why physicists, like myself, continue to be so excited about this, perhaps the final theory.

The gauge mediation models with a gravitino mass in the eV range is a quite attractive scenario which causes no cosmological/astrophysical problems. The model construction with such a light gravitino is, however, quite challenging and in most cases ends up with the problems with the suppressed gaugino mass, the vacuum instability and the Landau pole problems of the Standard Model gauge coupling constants. In this talk, I explain our proposal in which a gauge mediation model with the gravitino whose mass in the eV range is realized without having those problems.

In this talk I shall describe a general formalism based on $AdS_2/CFT_1$ correspondence that allows us to systematically calculate the entropy, index and other physical observables of an extremal black hole taking into account higher derivative and quantum corrections to the action. I shall also describe precise microscopic computation of the same quantities for a class of supersymmetric extremal black holes and compare this with the prediction of $AdS_2/CFT_1$ correspondence.

In this talk I shall describe a general formalism based on $AdS_2/CFT_1$ correspondence that allows us to systematically calculate the entropy, index and other physical observables of an extremal black hole taking into account higher derivative and quantum corrections to the action. I shall also describe precise microscopic computation of the same quantities for a class of supersymmetric extremal black holes and compare this with the prediction of $AdS_2/CFT_1$ correspondence.

In this talk I shall describe a general formalism based on $AdS_2/CFT_1$ correspondence that allows us to systematically calculate the entropy, index and other physical observables of an extremal black hole taking into account higher derivative and quantum corrections to the action. I shall also describe precise microscopic computation of the same quantities for a class of supersymmetric extremal black holes and compare this with the prediction of $AdS_2/CFT_1$ correspondence.

We discuss holographic models for the inflationary epoch. We show how cosmological observables such as the primordial spectrum and non-Gaussianities can be computed via computations of correlation functions of a dual three dimensional QFT (without gravity!) We present a general class of models that have the following universal features: (i) they have a nearly scale invariant spectrum of small amplitude primordial fluctuations, (ii) the scalar spectral index runs as alpha_s = - (n_s-1), (iii) the three point function of density perturbations is exactly equal to the sum of the local and equilateral form with f_{NL}^{local} = 6 f_{NL}^{equil} = 20/3.

We study time dependent couplings in conformal field theories using rotating probe branes in AdS X S spacetimes. We find that induced metrics on the brane worldvolumes develop horizons with characteristic Hawking temperatures even when there is no black hole in the bulk. This framework is used to obtain toy models for quantum quench.

Quantization of string theory on the AdS(3) backgrounds with the RR flux, such as AdS(3)xS(3)xT(4) or AdS(3)xS(3)xS(3)xS(1), is an unsolved problem. Since the sigma model on these backgrounds is classically integrable, one can try to implement powerful methods of integrability similar to those used to solve AdS(5)/CFT(4) and AdS(4)/CFT(3). I will describe the integrability approach to the AdS(3) backgrounds, emphasizing the differences to the better understood cases of AdS(5) and AdS(4).

A plethora of Higgsless models have been proposed and we are in the peculiar situation where Fermilab & LHC results will be extremely interesting whether or not the Higgs boson is found. I present here a model where one of the sacred assumption of quantum field theory (renormalizability) is dropped. A precise prescription for the removal of the divergences guarantees both unitarity and predictivity. Interestingly the model is consistent if the Power counting criterion is enforced in a weak form (Weak Power Counting). Among the novel features one notices an extra parameter (the ratio M_W/M_Z) but also a consistent accommodation of the Majorana neutrino mass.

Two-dimensional non-linear sigma models on some supergroup manifolds are conformal field theories whether the action includes a Wess-Zumino term or not. These models are relevant for the worldsheet description of string theory in Anti-de Sitter backgrounds with Ramond-Ramond fluxes. The current algebra is an useful tool to study these theories. In these lectures I will review the construction of the current algebra. Then I will discuss some applications to the computation of the spectrum and integrability.