Week 15.11.2009 – 21.11.2009

Motivated by recent work on frustrated spin chains and anyonic fusion chains, we define a 1D quantum Hamiltonian (based on the Temperley-Lieb algebra) which contains these models as special cases. This Hamiltonian contains a new integrable point with Z_2-symmetry, which we have solved exactly. In this talk, I will first explain the physical motivations and recall basic facts on the Temperley-Lieb algebra, a central object in 2D Statistical Mechanics. Then I will present analytical and numerical results for the phase diagram, and comment on perspectives in the fields of Condensed Matter Theory and Integrable Models.

A large family of interacting conformal field theories in four dimensions with N=2 supersymmetry was recently constructed by Gaiotto. Each gauge theory is associated to a Riemann surface with certain allowed singularities. In fact, it was proposed by Alday, Gaiotto and Tachikawa that the partition function of these theories (based on SU(2) gauge groups) is equal to correlation function in Liouville theory with central charge c=25. After reviewing these constructions I will turn to a detailed exploration of S-duality using loop operators: Wilson, 't Hooft and dyonic. I will explain the classification and evaluation of arbitrary loops in arbitrary theories and show how they transform into each-other under S-duality.

The dynamics of vortices and quasiparticles in holographic realizations of 2+1 dimensional strongly interacting systems are studied in the presence of magnetic field. The first part of the seminar will discuss holographic superconductors and the second part will discuss holographic realizations of Fermi surfaces.