Differential operator realization of the exceptional superalgebra \(D(2, 1;\alpha)\) and its application. (English) Zbl 1247.81422
Summary: We give the explicit expressions of the differential operator representations of the exceptional Lie superalgebra \(D(2, 1;\alpha )\). Based on these expressions, we construct free field realizations of the currents associated with \(D(2, 1;\alpha)\) at an arbitrary level \(k\).
MSC:
| 81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |
| 17A70 | Superalgebras |
| 17B25 | Exceptional (super)algebras |
| 81R15 | Operator algebra methods applied to problems in quantum theory |
| 81T13 | Yang-Mills and other gauge theories in quantum field theory |
| 81T30 | String and superstring theories; other extended objects (e.g., branes) in quantum field theory |
