Week 11.05.2015 – 17.05.2015

My starting point is a holographic model of the Kondo effect recently proposed by Erdmenger et. al., i.e. of a magnetic impurity interacting with a strongly coupled system. Specifically, I focus on the challenges of computing gravitational backreaction in this model, which demands a study of the Israel junction conditions. I present general results on these junction conditions, including analytical solutions for certain toy models, that may be relevant also more generally in the AdS/boundary CFT correspondence. Furthermore, similar junction conditions for a bulk Chern-Simons field appearing in the holographic Kondo model are discussed. I then focus on the computation and interpretation of entanglement entropy in this holographic model.

Hydrodynamic integrable systems are characterized by an infinite number of conserved quantities and can be described in terms of integrable partial differential equations. I will focus on the periodic Intermediate Long Wave (ILW) system, both at the classical and quantum level. The quantum system has not been solved yet, if not in a particular limit (the Benjamin-Ono limit) which is related to the AGT correspondence. In this talk I will show how a particular two dimensional N=(2,2) gauge theory on S^2 can be used to determine the spectrum of the quantum ILW system via Bethe Ansatz equations, as well as the norm of the eigenstates. In addition the partition function of this theory computes genus zero Gromov-Witten invariants for the ADHM instanton moduli space, thus relating quantum cohomology to quantum hydrodynamics.

We will discuss the construction of type IIA mirror a la Strominger Yau Zaslow prescription and its M-theory uplift in the delocalized limit {resulting in black M3-branes=asymptotically black M5-branes wrapping large integer sum of two-spheres in AdS_5xM_6} of type IIB backgrounds involving non-Kaehler resolved warped deformed conifolds in the presence of [fractional]D3 and wrapped D7-branes relevant to thermal QCD with fundamental quarks. We will show that the local T^3 relevant to SYZ mirror construction obeys the same constraint as the maximal T^2-invariant special Lagrangian three-cycle of deformed conifolds. We also discuss evaluation of the SU(3) structure torsion classes of the type IIB background and show its (approximate) Kaehlerity. We will also discuss thermodynamical/hydrodynamical properties as well as evaluation of a variety of transport coefficients {from correlation functions of gauge and metric fluctuations}, speed of sound and QCD deconfinement temperature consistent with lattice data.