Integer quantum hall effect and it's gravity dual

Abstract

If we take a bunch of electrons and restrict them to move in a two dimensional plane and turn on a strong magnetic field. This simple set up provides the setting for some of the most wonderful and surprising results in physics. These phenomena are known collectively as the quantum Hall effect. The Hall conductivity takes the quantised value. We started with building our understanding in classical and quantum Hall effect, then we calculated quantum mechanical analogous of conductivity known as Kubo formula. But our aim was to apply our knowledge and understanding to calculate conductivity in relativistic domain, for that we started with learning physics of relativity and then tried to look at some standard problems of relativity namely D3-branes solution in asymptotically flat background geometry. We took a metric for this solution, calculated its Born-Infeld action, and transforming the coordinates into Eddington Finkelstein coordinates and thus calculated longitudinal and transverse conductivity for two currents. Gaining the boost from these calculations we took a most general Bubbling geometry metric and to obtain the longitudinal and transverse conductivity we assumed a special case of half filling planes and got the curves of conductivity v/s magnetic field. These curves were asymptotically in nature.