String Seminars

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.

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.

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.