Chennai Mathematical Institute


2.30 pm,
Aspects of holography: mainly nAdS2 holography from dimensional reduction and non-relativistic holography for hvLif theories

Kedar S. Kolekar
IIT Kanpur.


In this talk, we will focus on our investigations of certain aspects of holography, in particular, nearly-AdS2 holography in certain theories of dilaton-gravity coupled to matter and non-relativistic holography in the context of hyperscaling violating Lifshitz theories.

We will begin by introducing hyperscaling violating Lifshitz (hvLif) spacetimes as the class of non-relativistic theories of our interest. Then we will briefly discuss certain hydrodynamic properties of hvLif theories, in particular, the shear diffusion and the shear viscosity to entropy density ratio for the bulk uncharged hvLif spacetimes. Charge can be added through an additional U(1) gauge field and extremal charged hvLif black branes acquire AdS2 in the near-horizon region of the geometry. Compactification of the transverse space, then leads to an effective description in terms of 2-dimensional dilaton-gravity coupled to matter. We will discuss the dynamics of nearly-AdS2 in these theories of dilaton-gravity obtained by dimensional reduction of extremal charged black branes in hvLif theories. These 2-dimensional theories are Jackiw-Teitelboim type models along with subleading corrections, the leading effects being captured by the Schwarzian action. Then we will consider a generalized class of 2-dimensional dilaton-gravity-matter theories arising from the reductions of higher dimensional gravity-matter theories. We will study holographic renormalization group (RG) flows ending at AdS2 fixed point in the infrared, in these 2-dimensional theories. We formulate a holographic c-function characterizing this RG flow and argue holographic c-theorem. We also analyze the RG flow equations and beta-functions by adapting the radial Hamiltonian formulation of holographic RG by de Boer, Verlinde and Verlinde.