Supersymmetric algebra of the massive supermembrane. (English) Zbl 1520.83075
Summary: In this paper, we obtain the explicit expression of the supersymmetric algebra associated with the recently proposed massive supermembrane including all surface terms. We formulate the theory as the limit of a supermembrane on a genus-two compact Riemann surface when one of the handles becomes a string attached to a torus. The formulation reduces to a supermembrane on a punctured torus with a “string spike” (in the sense of [B. De Wit et al., Nucl. Phys., B 320, No. 1, 135–159 (1989; doi:10.1016/0550-3213(89)90214-9)]), attached to it. In this limit, we identify all surface terms of the algebra and give the explicit expression of the Hamiltonian in agreement with the previous formulation of it. The symmetry under area preserving diffeomorphisms, connected and nonconnected to the identity, is also discussed. Only parabolic \(Sl(2, \mathbb{Z})\) discrete symmetries are preserved.
MSC:
| 83E50 | Supergravity |
| 53C12 | Foliations (differential geometric aspects) |
| 83C75 | Space-time singularities, cosmic censorship, etc. |
| 32J81 | Applications of compact analytic spaces to the sciences |
| 58D05 | Groups of diffeomorphisms and homeomorphisms as manifolds |
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