Coherent state construction of representations of \(\mathrm{osp}(2| 2)\) and primary fields of \(\mathrm{osp}(2| 2)\) conformal field theory. (English) Zbl 1138.81437
Summary: Representations of the superalgebra \(\mathrm{osp}(2| 2)\) and current superalgebra \(\mathrm{osp}(2| 2)^{(1)}_k\) in the standard basis are investigated. All finite-dimensional typical and atypical representations of \(\mathrm{osp}(2| 2)\) are constructed by the vector coherent state method. Primary fields of the non-unitary conformal field theory associated with \(\mathrm{osp}(2| 2)^{(1)}_k\) in the standard basis are obtained for arbitrary level \(k\).
MSC:
| 81R10 | Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations |
| 81R30 | Coherent states |
| 81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |
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