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 |
References:
[1] | Rozanski, L.; Saleur, H., Nucl. Phys. B, 376, 461 (1992) |
[2] | Isidro, J. M.; Ramallo, A. V., Nucl. Phys. B, 414, 715 (1994) · Zbl 1007.81542 |
[3] | Flohr, M. |
[4] | Efetov, K., Adv. Phys., 32, 53 (1983) |
[5] | Bernard, D. |
[6] | Mudry, C.; Chamon, C.; Wen, X.-G., Nucl. Phys. B, 466, 383 (1996) · Zbl 1002.81544 |
[7] | Maassarani, Z.; Serban, D., Nucl. Phys. B, 489, 603 (1997) · Zbl 0925.81328 |
[8] | Bassi, Z. S.; LeClair, A., Nucl. Phys. B, 578, 577 (2000) · Zbl 1037.82521 |
[9] | Guruswamy, S.; LeClair, A.; Ludwig, A. W.W., Nucl. Phys. B, 583, 475 (2000) · Zbl 0984.82029 |
[10] | Ludwig, A. W.W. |
[11] | Bhaseen, M. J.; Caux, J.-S.; Kogan, I. I.; Tsvelik, A. M., Nucl. Phys. B, 618, 465 (2001) · Zbl 0992.81098 |
[12] | Scheunert, M.; Nahm, W.; Rittenberg, V., J. Math. Phys., 18, 146 (1977) · Zbl 0354.17004 |
[13] | Marcu, M., J. Math. Phys., 21, 1284 (1980) · Zbl 0445.17004 |
[14] | Dobrev, V. K., (Hietarinta, J., Proceedings of the Symposium on Topological and Geometrical Methods in Field Theory, Espoo, Finland, June 4-18, 1986 (1987), World Scientific: World Scientific Singapore), 93 |
[15] | Kobayashi, K., Z. Phys. C, 61, 105 (1994) |
[16] | Bowcock, P.; Taormina, A., Commun. Math. Phys., 185, 467 (1997) · Zbl 0882.17014 |
[17] | Semikhatov, A. M., Theor. Math. Phys., 112, 949 (1997) |
[18] | Ding, X. M.; Gould, M. D.; Mewton, C. J.; Zhang, Y.-Z., J. Phys. A, 36, 7649 (2003) · Zbl 1048.81051 |
[19] | Bowcock, P.; Koktava, R.-L. K.; Taormina, A., Phys. Lett. B, 388, 303 (1996) |
[20] | Rasmussen, J., Nucl. Phys. B, 510, 688 (1998) · Zbl 0953.81028 |
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