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On-shell Action for Bubbling Geometries

Matsuo Sato
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Abstract

We study the half-BPS sector of the AdS/CFT correspondence. In the full sector of the correspondence, on-shell actions in type IIB supergravity have been 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: an 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.

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Matsuo Sato. 2007-06-26. On-shell Action for Bubbling Geometries. https://doi.org/10.1143/ptp.118.337

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