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Prog. Theor. Phys. Vol. 118 No. 2 (2007) pp. 337-346
On-Shell Action for Bubbling Geometries
Matsuo Sato
Department of Physics, Kyoto University, Kyoto 606-8502, Japan
(Received May 1, 2007)
Abstract:
We study the half-BPS sector of the AdS/CFT correspondence. In the full sector
of this correspondence, on-shell actions in type IIB supergravity have played
crucial roles, for example in the GKP-Witten relation. We derive, therefore, an
on-shell action that reproduces a class of half-BPS solutions found by Lin,
Lunin and Maldacena. These solutions describe the bubbling geometries in the
supergravity. We show that this on-shell action for the LLM solutions is dual
to the classical limit of an observable of the N free fermions in a harmonic
oscillator potential in 1+1 dimensions. The observable consists of three parts:
the expectation value of the total energy, matrix elements of the momentum
squared, and matrix elements of the position squared. Our results suggest that
there exists a holographic correspondence on a two-dimensional surface in the
bubbling geometries.
URL :
http://ptp.ipap.jp/link?PTP/118/337/
DOI : 10.1143/PTP.118.337
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