23 research outputs found
BPS States in Omega Background and Integrability
We reconsider string and domain wall central charges in N=2 supersymmetric
gauge theories in four dimensions in presence of the Omega background in the
Nekrasov-Shatashvili (NS) limit. Existence of these charges entails presence of
the corresponding topological defects in the theory - vortices and domain
walls. In spirit of the 4d/2d duality we discuss the worldsheet low energy
effective theory living on the BPS vortex in N=2 Supersymmetric Quantum
Chromodynamics (SQCD). We discuss some aspects of the brane realization of the
dualities between various quantum integrable models. A chain of such dualities
enables us to check the AGT correspondence in the NS limit.Comment: 48 pages, 10 figures, minor changes, references added, typos
correcte
Bootstrapping the superconformal index with surface defects
The analytic properties of the N = 2 superconformal index are given a
physical interpretation in terms of certain BPS surface defects, which arise as
the IR limit of supersymmetric vortices. The residue of the index at a pole in
flavor fugacity is interpreted as the index of a superconformal field theory
without this flavor symmetry, but endowed with an additional surface defect.
The residue can be efficiently extracted by acting on the index with a
difference operator of Ruijsenaars-Schneider type. By imposing the
associativity constraints of S-duality, we are then able to evaluate the index
of all generalized quiver theories of type A, for generic values of the three
superconformal fugacities, with or without surface defects.Comment: 60 pages, 7 figure
Dynamical Mean-Field Theory
The dynamical mean-field theory (DMFT) is a widely applicable approximation
scheme for the investigation of correlated quantum many-particle systems on a
lattice, e.g., electrons in solids and cold atoms in optical lattices. In
particular, the combination of the DMFT with conventional methods for the
calculation of electronic band structures has led to a powerful numerical
approach which allows one to explore the properties of correlated materials. In
this introductory article we discuss the foundations of the DMFT, derive the
underlying self-consistency equations, and present several applications which
have provided important insights into the properties of correlated matter.Comment: Chapter in "Theoretical Methods for Strongly Correlated Systems",
edited by A. Avella and F. Mancini, Springer (2011), 31 pages, 5 figure