Chiral and real N=2 supersymmetric ℓ-conformal Galilei algebras

Journal Article · Sun Sep 15 04:00:00 EDT 2013 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4820481· OSTI ID:22217994

Aizawa, N. ^[1]; Kuznetsova, Z. ^[2]; Toppan, F. ^[3]

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1. Department of Mathematics and Information Sciences, Graduate School of Science, Osaka Prefecture University, Nakamozu Campus, Sakai, Osaka 599-8351 (Japan)
2. UFABC, Rua Santa Adélia 166, Bangu, cep 09210-170, Santo André, SP (Brazil)
3. CBPF, Rua Dr. Xavier Sigaud 150, Urca, cep 22290-180, Rio de Janeiro, RJ (Brazil)

Inequivalent N=2 supersymmetrizations of the ℓ-conformal Galilei algebra in d-spatial dimensions are constructed from the chiral (2, 2) and the real (1, 2, 1) basic supermultiplets of the N=2 supersymmetry. For non-negative integer and half-integer ℓ, both superalgebras admit a consistent truncation with a (different) finite number of generators. The real N=2 case coincides with the superalgebra introduced by Masterov, while the chiral N=2 case is a new superalgebra. We present D-module representations of both superalgebras. Then we investigate the new superalgebra derived from the chiral supermultiplet. It is shown that it admits two types of central extensions, one is found for any d and half-integer ℓ, and the other only for d= 2 and integer ℓ. For each central extension, the centrally extended ℓ-superconformal Galilei algebra is realized in terms of its super-Heisenberg subalgebra generators.

• OSTI ID: 22217994
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 9 Vol. 54; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ALGEBRA
CHIRAL SYMMETRY
CHIRALITY
SUPERMULTIPLETS
SUPERSYMMETRY