Theory of random matrices plays a crucial role both in mathematics and physics. The field was initiated almost a century ago by statisticians and introduced in physics in the 50s-60s by Wigner and Dyson. The theory has diverse application in different branches in physics and mathematics. We focus on a subset of random matrix theory : unitary matrix models (UMMs). Partition functions of different super-symmetric gauge theories, in particular Chern-Simons theories on certain manifolds boil down to UMMs. Different topological string theories reduce to UMM. These models also have applications in a broad class of condensed matter systems. Therefore, UMM is a useful tool to solve varieties of physical systems. Our main goal is to use the versatility of UMM to explore a dual quantum mechanical description of string theory (quantum gravity). More
Black holes are intriguing objects in general relativity which exhibit thermodynamic behavior and can be assigned temperature and entropy. Understanding its thermodynamic properties is a fundamental issue in black hole physics. Surprisingly, recently the study of black holes has also been relevant to explore the properties of realistic theories such as QCD, plasma and superconductors in the context of the gauge/gravity correspondence.
Black holes first appeared as classical solutions of general relativity. Almost a century ago, Schwarzschild presented the first explicit black hole solution. More general black hole solutions were only discovered much later. All black hole solutions have a point-like curvature singularity, which is separated from the outside world by a hypothetical surface known as the event horizon.
Low energy limit of string theory gives rise to gravity coupled to other fields. As a results these theories have black hole solutions. In this way string theory gives a framework for studying classical and quantum properties of black holes. Interestingly, study of them has led to new results in string theory. More
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It is well known that non-relativistic incompressible viscous fluids are described by the Navier-Stokes equations. Fluid dynamical evolution of a system shows many challenging properties like turbulence whose detailed understanding is still missing. The hydrodynamic behavior of the system is characterized by a set of transport coefficients, like shear viscosity, bulk viscosity etc. A holographic description of the fluid dynamical system provides a new perspective on the problem. One can apply this toolkit to compute different transport coefficients of strongly coupled plasma. Although, the fluid/gravity correspondence predicts properties of a relativistic conformal fluid, the generalization of the correspondence to non-relativistic (also non-conformal) systems exists and we will discuss about those issues subsequently.
After Relativistic Heavy Ion Collider (RHIC) experiments, the study of shear viscosity to entropy density ratio of gauge theory plasma has developed lots of attention. The QGP (Quark-Gluon Plasma) produced at RHIC behaves like viscous fluid with very small shear viscosity coefficient (near-perfect fluid). Such a low ratio of shear viscosity to entropy density is very hard to describe with conventional method. Usual perturbative gauge theory computations or lattice gauge theory technique are not applicable to explain RHIC results. Holographic techniques (motivated from the AdS/CFT correspondence) to compute hydrodynamic transport coefficients exhibit a remarkable quantitative agreement with those arising from numerical fits to RHIC data. More coming up
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