Holographic renormalization for z = 2 Lifshitz spacetimes from AdS

Chemissany, Wissam; Geissbühler, David; Hartong, Jelle; Rollier, Blaise (2012). Holographic renormalization for z = 2 Lifshitz spacetimes from AdS. Classical and quantum gravity, 29(23), p. 235017. Bristol, UK: Institute of Physics Publishing IOP 10.1088/0264-9381/29/23/235017

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Lifshitz spacetimes with the critical exponent z = 2 can be obtained by the dimensional reduction of Schrödinger spacetimes with the critical exponent z = 0. The latter spacetimes are asymptotically AdS solutions of AdS gravity coupled to an axion–dilaton system and can be uplifted to solutions of type IIB supergravity. This basic observation is used to perform holographic renormalization for four-dimensional asymptotically z = 2 locally Lifshitz spacetimes by the Scherk–Schwarz dimensional reduction of the corresponding problem of holographic renormalization for five-dimensional asymptotically locally AdS spacetimes coupled to an axion–dilaton system. We can thus define and characterize a four-dimensional asymptotically locally z = 2 Lifshitz spacetime in terms of five-dimensional AdS boundary data. In this setup the four-dimensional structure of the Fefferman–Graham expansion and the structure of the counterterm action, including the scale anomaly, will be discussed. We find that for asymptotically locally z = 2 Lifshitz spacetimes obtained in this way, there are two anomalies each with their own associated nonzero central charge. Both anomalies follow from the Scherk–Schwarz dimensional reduction of the five-dimensional conformal anomaly of AdS gravity coupled to an axion–dilaton system. Together, they make up an action that is of the Horava–Lifshitz type with a nonzero potential term for z = 2 conformal gravity.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Institute of Theoretical Physics

UniBE Contributor:

Geissbühler, David; Hartong, Jelle and Rollier, Blaise

Subjects:

500 Science > 530 Physics

ISSN:

0264-9381

Publisher:

Institute of Physics Publishing IOP

Language:

English

Submitter:

Esther Fiechter

Date Deposited:

04 Oct 2013 14:42

Last Modified:

09 Nov 2016 10:50

Publisher DOI:

10.1088/0264-9381/29/23/235017

Web of Science ID:

000311101800019

BORIS DOI:

10.7892/boris.17032

URI:

https://boris.unibe.ch/id/eprint/17032 (FactScience: 224751)

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