On AdS 2 holography from redux, renormalization group flows and c -functions

Kolekar, Kedar (0000 0004 1777 263X, Chennai Mathematical Institute, SIPCOT IT Park, Siruseri, 603103, India) ; Narayan, K. (0000 0004 1777 263X, Chennai Mathematical Institute, SIPCOT IT Park, Siruseri, 603103, India)

10 February 2019

Abstract: Extremal black branes upon compactification in the near horizon throat region are known to give rise to AdS 2 dilaton-gravity-matter theories. Away from the throat region, the background has nontrivial profile. We interpret this as holographic renormalization group flow in the 2-dim dilaton-gravity-matter theories arising from dimensional reduction of the higher dimensional theories here. The null energy conditions allow us to formulate a holographic c-function in terms of the 2-dim dilaton for which we argue a c-theorem subject to appropriate boundary conditions which amount to restrictions on the ultraviolet theories containing these extremal branes. At the infrared AdS 2 fixed point, the c-function becomes the extremal black brane entropy. We discuss the behaviour of this inherited c-function in various explicit examples, in particular compactified nonconformal branes, and compare it with other discussions of holographic c-functions. We also adapt the holographic renormalization group formulated in terms of radial Hamiltonian flow to 2-dim dilaton-gravity-scalar theories, which while not Wilsonian, gives qualitative insight into the flow equations and β-functions.


Published in: JHEP 1902 (2019) 039
Published by: Springer/SISSA
DOI: 10.1007/JHEP02(2019)039
arXiv: 1810.12528
License: CC-BY-4.0



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