Quantum Fields and Strings

The massless fields of closed string theory on toroidal backgrounds naturally depend on coordinates dual to momentum and coordinates dual to winding. Their dynamical theory, which contains gravitation, must include diffeomorphism and dual diffeomorphism invariance. We begin a serious attempt to construct this generalized form of field theory.

We study a simple model of a black hole in AdS and obtain a holographic description of the region inside the horizon,as seen by an infalling observer. For D-brane probes, we construct a map from physics seen by an infalling observer to physics seen by an asymptotic observer that can be generalized to other AdS black holes.

Gauge theories with deformed products of fields in the lagrangian constitute an interesting generalization of the gauge/string duality. We review a systematic procedure to find the string duals of such theories, called the TsT transformation, and illustrate its properties by means of a few examples.

Recently methods of integrability were shown to be useful for solving gauge theories in various dimensions. I will make an introduction into integrability in two dimensions and demonstrate how the integrability works also for some three and four dimensional gauge theories.

Holographic superconductors provide tractable models for the onset of superconductivity in strongly coupled theories. They have some features in common with experimentally studied nonconventional superconductors. I will review the physics of holographic superconductors and go on to show that many such models are to be found in the string landscape of AdS_4 vacua.

A simple model for chaotic inflation in supergravity is proposed. The model is N = 1 supersymmetric massive U(1)gauge theory via the Stuckelberg superfield and gives rise to D-term inflation with a quadratic term of inflaton in the potential. The Fayet-Iliopoulos field plays a role of the inflaton. It is also discussed to give rise to successful reheating and leptogenesis through the inflaton decay.

The Rozansky-Witten model is a topological sigma-model in three dimensions whose target is a hyper-Kahler manifold. Upon compactification to 2d it reduces to the B-model with the same target. Boundary conditions for the Rozansky-Witten model can be regarded as a 3d generalization of B-branes. While branes form a category, boundary conditions in a 3d TFT form a 2-category. I will describe the structure of this 2-category for the Rozansky-Witten model and its connection with a categorification of deformation quantization. I will also discuss defects of codimension 1 (domain walls) and defects of codimension 2 (line operators) in the Rozansky-Witten model.

Brane Tilings are known to describe the largest known class of SCFT's in 3+1 dimensions. There is a well established formalism to find AdS_5 x SE_5 duals to these SCFT's and to compare results on both sides. This talk extends this formalism to 2+1 dimensional SCFT's, living on the world volume of M2 branes, which are dual to AdS_4 x SE_7 backgrounds of M theory. The SCFT's are quiver gauge theories with 4 supercharges (N=2 in 2+1 dimensions) and Chern Simons (CS) couplings. They admit a moduli space of vacuum configurations which is a CY4 cone over SE_7. The talk will go over the formalism and look at several examples in detail. The computation of scaling dimensions will be mentioned and relations to regular toric Fano 3-folds if time permits.

Motivated by recent mathematical developements in non-commutative Donaldson-Thomas theory, we construct a new statistical mechanicalmodel of crystal melting to count BPS bound states of D0 and D2 branes on a single D6 brane wrapping an arbitrary toric Calabi-Yau threefold. We also discuss the wall crossing phenomena, which are crucial for the proper understanding of the relation between the crystal melting and the topological string theory.

We derive a universal upper bound on the weight of the lowest primary operator in any two-dimensional conformal field theory with a given central charge. Translated into gravitational language using the AdS/CFT dictionary, our result proves rigorously that the lightest massive state in any theory of 3D gravity and matter with negative cosmological constant can be no heavier than a particular function the cosmological constant and the Planck scale. For a large AdS space, the lower bound approaches the mass of the lightest BTZ black hole. The derivation applies at finite central charge and does not rely on an asymptotic expansion at large central charge, or on any use of semiclassical or bulk physics. Neither does our proof rely on any special property of the CFT such as supersymmetry or holomorphic factorization. The only assumptions are unitarity, modular invariance, and a discrete spectrum. Our proof firmly demonstrates for the first time that there exists a universal center-of-mass energy beyond which a theory of 'pure' quantum gravity can never consistently be extended.

In the past couple of years many new developments have been made in the techniques used for computing one-loop gauge theory amplitudes. These developments have mainly involved exploiting generalized unitarity techniques to construct the coefficients of the basis integral functions which make up a one-loop amplitude. I will outline these new developments along with their application to both QCD and N=8 supergravity amplitudes.