Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2005-02-10
JHEP 0508 (2005) 052
Physics
High Energy Physics
High Energy Physics - Theory
28 pages, 2 figures, epsf;(v3) eq. (3.3) clarified and notationally simplified; version to appear in JHEP
Scientific paper
10.1088/1126-6708/2005/08/052
We discuss collective coordinate quantization of the half-BPS geometries of Lin, Lunin and Maldacena (hep-th/0409174). The LLM geometries are parameterized by a single function $u$ on a plane. We treat this function as a collective coordinate. We arrive at the collective coordinate action as well as path integral measure by considering D3 branes in an arbitrary LLM geometry. The resulting functional integral is shown, using known methods (hep-th/9309028), to be the classical limit of a functional integral for free fermions in a harmonic oscillator. The function $u$ gets identified with the classical limit of the Wigner phase space distribution of the fermion theory which satisfies u * u = u. The calculation shows how configuration space of supergravity becomes a phase space (hence noncommutative) in the half-BPS sector. Our method sheds new light on counting supersymmetric configurations in supergravity.
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