Ilmar Gahramanov

Anisotropic hydrodynamics, holography and the chiral magnetic effect

We discuss a possible dependence of the chiral magnetic effect (CME) on the elliptic flow coefficient v2. We first study this in a hydrodynamic model for a static anisotropic plasma with multiple anomalous U(1) currents. In the case of two charges, one axial and one vector, the CME formally appears as a first-order transport coefficient in the vector current. We compute this transport coefficient and show its dependence on v2. We also determine the CME-coefficient from first-order corrections to the dual AdS background using the fluid-gravity duality. For small anisotropies, we find numerical agreement with the hydrodynamic result.

The star-triangle relation and 3d superconformal indices

A bstractSuperconformal indices of 3dN=2

Superconformal indices and partition functions for supersymmetric field theories

\mathcal{N}=2

Integral pentagon relations for 3d superconformal indices

supersymmetric field theories are investigated from the Yang-Baxter equation point of view. Solutions of the star-triangle relation, vertex and IRF Yang-Baxter equations are expressed in terms of the q-special functions associated with these 3d indices. For a two-dimensional monopole-spin system on the square lattice a free energy per spin is explicitly determined. Similar to the partition functions, superconformal indices of 3d theories with the chiral symmetry breaking reduce to Dirac delta functions with the support on chemical potentials of the preserved flavor groups.Superconformal indices of 3d N = 2 supersymmetric field theories are investigated from the Yang-Baxter equation point of view. Solutions of the star-triangle relation, vertex and IRF Yang-Baxter equations are expressed in terms of the q-special functions associated with these 3d indices. For a two-dimensional monopole-spin system on the square lattice a free energy per spin is explicitly determined. Similar to the partition functions, superconformal indices of 3d theories with the chiral symmetry breaking reduce to Dirac delta functions with the support on chemical potentials of the preserved flavor groups.

Remark on the Dunne-Ünsal relation in exact semiclassics

A bstractRecently Kashaev, Luo and Vartanov, using the reduction from a fourdimensional superconformal index to a three-dimensional partition function, found a pentagon identity for a special combination of hyperbolic Gamma functions. Following their idea we have obtained a new pentagon identity for a certain combination of so-called tetrahedron indices arising from the equality of superconformal indices of dual three-dimensional

Mathematical structures behind supersymmetric dualities

\mathcal{N}

Extended global symmetries for 4D

= 2 supersymmetrictheoriesandgiveamathematicalproofofit.

\mathcal{N}=1

Recently there was a substantial progress in understanding of supersymmetric theories (in particular, their BPS spectrum) in space-times of different dimensions due to the exact computation of superconformal indices and partition functions using localization method. Here we discuss a connection of 4d superconformal indices and 3d partition functions using a particular example of supersymmetric theories with matter in antisymmetric representation.