The algebra of supertraces for (2 + 1) super de Sitter gravity

Journal Article · Mon Sep 21 00:00:00 EDT 1992 · Modern Physics Letters A; (Singapore)

DOI:https://doi.org/10.1142/S0217732392002172· OSTI ID:6967199

Urrutia, L F ^[1]; Waelbroeck, H ^[2]; Zertuche, F ^[3]

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1. Centro de Estudios Cientificos de Santiago, Casilla 16443, Santiago 9 (Chile)
2. Inst. de Ciencias Nucleares, Univ. Nacional Autonoma de Mexico, Circuito Exterior, C.U., 04510 Mexico, D.F. (Mexico)
3. Centro Nacional de Investigacion y Desarrollo Tecnologico, Interior Internado Palmira s/n, A.P. 4-224, 62431 Cuernavaca, Morelos (Mexico)

In this paper, the authors calculate the algebra of the observables for 2 + 1 super de Sitter gravity, for one genus of the spatial surface. The algebra turns out to be an infinite Lie algebra subject to nonlinear constraints. The authors solve the constraints explicitly in terms of five independent complex supertraces. These variables are the true degrees of freedom of the system and their quantized algebra generates a new structure which we refer to as a central extension of the quantum algebra SU(2)[sub q].

• OSTI ID: 6967199
• Journal Information: Modern Physics Letters A; (Singapore), Vol. 7:29; ISSN 0217-7323
• Country of Publication: United States
• Language: English

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