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

• Published in: The journal of high energy physics Vol. 2019; no. 2; pp. 1 - 38
• Main Authors: Kolekar, Kedar S, Narayan, K
• Format: Journal Article
• Language: English
• Published: Heidelberg Springer Nature B.V 01.02.2019; SpringerOpen
• Subjects: 2D Gravity; Boundary conditions; Branes; Dilatons; Fixed points (mathematics); Flow equations; Gauge-gravity correspondence; Gravitation; High energy physics; Holography; Holography and condensed matter physics (AdS/CMT); Throats
• ISSN: 1029-8479
• DOI: 10.1007/JHEP02(2019)039

Extremal black branes upon compactification in the near horizon throat region are known to give rise to AdS2 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 AdS2 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.