Holographic renormalization for z=2 Lifshitz spacetimes from AdS

TY - JOUR

T1 - Holographic renormalization for z=2 Lifshitz spacetimes from AdS

AU - Chemissany, W.

AU - Geissbuehler, D.

AU - Hartong, Jelle

AU - Rollier, B.

PY - 2012/12/7

Y1 - 2012/12/7

N2 - 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.

AB - 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.

U2 - 10.1088/0264-9381/29/23/235017

DO - 10.1088/0264-9381/29/23/235017

M3 - Journal article

SN - 0264-9381

VL - 29

SP - 235017

JO - Classical and Quantum Gravity

JF - Classical and Quantum Gravity

IS - 23

ER -