Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2007-03-07
Prog.Theor.Phys.118:337-346,2007
Physics
High Energy Physics
High Energy Physics - Theory
12 pages, 3 figures, v2: references added, v3: section 3, 4 and 5 improved, a reference and a figure added, typos corrected
Scientific paper
10.1143/PTP.118.337
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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