On axiomatic aspects of N=2 vertex superalgebras with odd formal variables, and deformations of N=1 vertex superalgebras
| dc.creator | Barron, Katrina | |
| dc.date | 2007-10-30 | |
| dc.date.accessioned | 2026-07-07T08:39:38Z | |
| dc.date.available | 2026-07-07T08:39:38Z | |
| dc.description | The notion of "N = 2 vertex superalgebra with two odd formal variables" is presented, the main axiom being a Jacobi identity with odd formal variables in which an N=2 superconformal shift is incorporated into the usual Jacobi identity for a vertex superalgebra. It is shown that as a consequence of these axioms, the N=2 vertex superalgebra is naturally a representation of the Lie algebra isomorphic to the three-dimensional algebra of superderivations with basis consisting of the usual conformal operator and the two N=2 superconformal operators. The notion of N=2 Neveu-Schwarz vertex operator superalgebra with two odd formal variables is introduced, and consequences of this notion are derived. Various other formulations of the notion of N=2 (Neveu-Schwarz) vertex (operator) superalgebra appearing in the mathematics and physics literature are discussed, and several mistakes in the literature are noted and corrected. The notion of ``N=2 (Neveu-Schwarz) vertex (operator) superalgebra with one odd formal variable" is formulated. It is shown that this formulation naturally arises from alternate notions of N=1 superconformality and the continuous deformation of an N=1 (Neveu-Schwarz) vertex (operator) superalgebra with one odd formal variable. This notion is formulated to reflect the underlying N=1 superanalytic geometry, and it is shown that the equivalence of the notions of N=2 (Neveu-Schwarz) vertex (operator) superalgebra with one and with two odd formal variables reflects the equivalence of N=2 superconformal and N=1 superanalytic geometry. In particular we prove that the group of formal N=2 superconformal functions vanishing at zero and invertible in a neighborhood of zero is isomorphic to a certain subgroup of N=1 superanalytic functions vanishing at zero and invertible in a neighborhood of zero. | |
| dc.description | 94 pages | |
| dc.identifier | https://arxiv.org/abs/0710.5755 | |
| dc.identifier | http://arxiv.org/abs/0710.5755 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/141138 | |
| dc.subject | Quantum Algebra | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | Mathematical Physics | |
| dc.subject | 17B69; 17B81; 81R10; 81T40 | |
| dc.title | On axiomatic aspects of N=2 vertex superalgebras with odd formal variables, and deformations of N=1 vertex superalgebras | |
| dc.type | text |