Quantum Fields and Strings

By using the AdS/CFT duality, the computation of MSYM scattering amplitudes at strong coupling boils down to the computation of minimal areas on AdS_5 with certain boundary conditions. Unfortunately, this seems to be a hard problem. In this talk we show how one can make progress by restricting to AdS_3.

I review the status of (open covariant) cubic superstring field theories, their successes and their problems. I then propose a new superstring field theory, which avoids previous problems. The picture number is not restricted in this theory and the NS and Ramond sectors are naturally unified. Constructing the BV master action is straightforwards and leads to a theory which is defined in the whole Hilbert space, i.e., including all ghost and picture numbers and all the relevant sectors. When (partially) gauge fixed and restricted to the NS sector, this new theory reduces to the old one. Hence, all the good known properties of the old one are shared by the new theory.

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.