TY - JOUR

T1 - Polyakov formulas for GJMS operators from AdS/CFT

AU - Díaz, Danilo E.

PY - 2008/7/1

Y1 - 2008/7/1

N2 - We argue that the AdS/CFT calculational prescription for double-trace deformations leads to a holographic derivation of the conformal anomaly, and its conformal primitive, associated to the whole family of conformally covariant powers of the Laplacian (GJMS operators) at the conformal boundary. The bulk side involves a quantum 1-loop correction to the SUGRA action and the boundary counterpart accounts for a sub-leading term in the large-N limit. The sequence of GJMS conformal Laplacians shows up in the two-point function of the CFT operator dual to a bulk scalar field at certain values of its scaling dimension. The restriction to conformally flat boundary metrics reduces the bulk computation to that of volume renormalization which renders the universal type A anomaly. In this way, we directly connect two chief roles of the Q-curvature: the main term in Polyakov formulas on one hand, and its relation to the Poincare metrics of the Fefferman-Graham construction, on the other hand. We find agreement with previously conjectured patterns including a generic and simple formula for the type A anomaly coefficient that matches all reported values in the literature concerning GJMS operators, to our knowledge.

AB - We argue that the AdS/CFT calculational prescription for double-trace deformations leads to a holographic derivation of the conformal anomaly, and its conformal primitive, associated to the whole family of conformally covariant powers of the Laplacian (GJMS operators) at the conformal boundary. The bulk side involves a quantum 1-loop correction to the SUGRA action and the boundary counterpart accounts for a sub-leading term in the large-N limit. The sequence of GJMS conformal Laplacians shows up in the two-point function of the CFT operator dual to a bulk scalar field at certain values of its scaling dimension. The restriction to conformally flat boundary metrics reduces the bulk computation to that of volume renormalization which renders the universal type A anomaly. In this way, we directly connect two chief roles of the Q-curvature: the main term in Polyakov formulas on one hand, and its relation to the Poincare metrics of the Fefferman-Graham construction, on the other hand. We find agreement with previously conjectured patterns including a generic and simple formula for the type A anomaly coefficient that matches all reported values in the literature concerning GJMS operators, to our knowledge.

KW - AdS-CFT correspondence

KW - Anomalies in field and string theories

UR - http://www.scopus.com/inward/record.url?scp=49849102218&partnerID=8YFLogxK

U2 - 10.1088/1126-6708/2008/07/103

DO - 10.1088/1126-6708/2008/07/103

M3 - Article

AN - SCOPUS:49849102218

VL - 2008

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 7

M1 - 103

ER -