Quantum Fields and Strings

The dynamics of fluids is a long standing challenge that remained as an unsolved problem for centuries. Understanding its main features, chaos and turbulence, is likely to provide an understanding of the principles and non-linear dynamics of a large class of systems far from equilibrium. We consider a conceptually new viewpoint to study these features using black hole dynamics. Since the gravitational field is characterized by a curved geometry, the gravity variables provide a geometrical framework for studying the dynamics of fluids: A geometrization of turbulence. We present new experimental predictions for relativsitic and non-relativistic turbulent flows and for heavy ion collisions.

Single-sector supersymmetry breaking models provide a unified explanation of two of the central mysteries of fundamental physics: the Planck/Weak hierarchy and the masses and mixings of the Standard Model particles. In this class of models, the flavor hierarchy is generated by quark and lepton compositeness, with the composites emerging from the same sector that dynamically breaks supersymmetry. In this seminar I will describe the first calculable, via a weakly coupled dual description, realization of this scenario. In the second part, I will explain how String Theory provides, via the gauge/gravity correspondence, another computational tool for handling the kind of strongly coupled gauge theories that arise in this context.

We discuss holographic duals of strongly interacting gauge theories which show properties of p-wave superfluids which in addition to an Abelian symmetry also break the spatial rotational symmetry. The gravity duals of these superfluid states are black hole solutions with a vector hair which we construct in a non-Abelian Einstein-Yang-Mills theory and in the D3/D7 brane setup. The latter allows us to identify the dual field theory explicitly. After we constructed the vector hair state we study the conductivity and shear viscosity which is non-universal due to the breaking of the rotational symmetry.

This talk will focus on hypermultiplet moduli spaces of various N=2 supersymmetric gauge theories in (3+1)d. In the first part of the talk, we discuss the moduli space of instantons on C^2. For the classical groups, the ADHM construction of the moduli space can be realised on the Higgs branch of N=2 gauge theories on D3-branes probing D7-branes. No known construction is available for exceptional groups. We go over the computation of Hilbert series for the one instanton moduli space and show that it is possible to count all chiral operators on the moduli space even though a Lagrangian is not known for exceptional gauge groups. In the second part, we discuss a class of N=2 gauge theories on two M5-branes wrapping Riemann surfaces. This talk will go over Hilbert series for the hypermultiplet moduli space of such theories and show that it is possible to count all chiral operators on the hypermultiplet moduli space for any genus and any number of punctures of the Riemann surface.

We give a detailed derivation of a supersymmetric configuration of wrapped D5-branes on a two-cycle of a warped resolved conifold. Our analysis reveals that the resolved conifold should support a non-Kahler metric with an SU(3) structure. We use this as a starting point of the geometric transition in type IIB theory. A mirror, and a subsequent flop transition using an intermediate M-theory configuration with a G2 structure, gives rise to the complete IR geometric transition in type IIA theory. A further mirror transformation gives the type IIB gravity dual of the IR gauge theory on the wrapped D5-branes. Expectedly non-Kahler deformations of the resolved and the deformed conifolds appear as the gravity duals of the confining gauge theories in type IIA and type IIB theories respectively, although in more generic cases these manifolds could also be non-geometric. In the local limit we reproduce precisely the scenarios presented in our earlier works. Our present work should therefore be viewed as providing a supergravity proof of geometric transitions in the full global scenarios in type II theories.

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 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).

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.

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.