Abstract
Explicit representations of super-Kac-Moody algebra are constructed in terms of 2d-free fermions which form a non-linear representation of supersymmetry with the fermions grouped with the generators of the algebra into superfields. It is shown how the most general construction of this type corresponds to homogeneous spacesG/H and how supersymmetry alone is responsible for that structure.
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Kac, V.: Math. USSR Izv.2, 1271 (1968)
Moody, R.: J. Algebra10, 211 (1968)
Kac, V.: Infinite dimensional Lie algebras. Boston: Birkhäuser 1983
Bardakci, K., Halpern, M.B.: New dual quark models. Phys. Rev. D3, 2493 (1971)
Halpern, M.B.: Quantum “solitons” which areSU(N) fermions. Phys. Rev. D12, 1684 (1975)
Frenkel, I.B.: Spinor representations of affine Lie algebras. Proc. Nat. Acad. Sci. USA, 6303 (1980)
Witten, E.: Non-abelian bosonization in two dimensions. Commun. Math. Phys.92, 455 (1984)
Wess, J., Zumino, B.: Consequences of anomalous Ward identities. Phys. Lett.37 B, 95 (1971)
Knizhnik, V.G., Zamolodchikov, A.M.: Current algebra and Wess-Zumino model in two dimensions. Nucl. Phys. B247, 83 (1984)
Friedan, D.: Recent advances in field theory and statistical mechanics. Les Houches Session XXXIX, Zuber, J.B., Stora, R. (eds.). Amsterdam: Elsevier 1984
Belavin, A.A., Polyakov, A.M., Zamolodchikov, A.M.: Infinite conformal symmetry in two-dimensional quantum field theory. Nucl. Phys. B241, 333 (1984)
Curtright, T., Zachos, C.: Geometry, topology, and supersymmetry in nonlinear models. Phys. Rev. Lett.53, 1799 (1984)
Rohm, R.: Princeton Preprint (October 1984)
di Vecchia, P., Knizhnik, V.G., Petersen, J.L., Rossi, P.: Nucl. Phys. B252, 701 (1985)
Windey, P.: Unpublished
Goddard, P., Olive, D.: Nucl. Phys. B
Neveu, A., Schwarz, J.: Factorizable dual model of pions. Nucl. Phys. B31, 86 (1971)
Ramond, P.: Dual theory for free fermions. Phys. Rev. D3, 2415 (1971)
Antoniadis, I., Bachas, C., Kounnas, C., Windey, P.: Slac preprint SLAC-PUB-3789
Virasoro, M.: Subsidiary conditions and ghosts in dual-resonance models. Phys. Rev. D1, 2933 (1970)
Bershadsky, M.A., Knizhnik, V.G., Teitelman, M.G.: Superconformal symmetry in two dimensions. Phys. Lett. B151, 31 (1985)
Friedan, D., Qiu, Z., Shenker, S.: Superconformal invariance in two dimensions and the tricritial Ising model. Phys. Lett. B151, 37 (1985)
See for example, Kobayashi, S., Nomizu, K.: Foundations of differential geometry (I, II). New York: Interscience 1969
This part of our results overlaps with work by P. Goddard, A. Kent, and D. Olive (preprint in preparation, private communication) and is a generalization to the supersymmetric case of their observation that the constraint (25) leads to symmetric space, see Goddard, P., Nahm, W., Olive, D.: Imperial/TP/84-85/25 (1985)
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Communicated by G. Parisi
This work was supported by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, Division of High Energy Physics of the U.S. Department of Energy under Contracts DE-AC03-76SF00098
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Windey, P. Super-Kac-Moody algebras and supersymmetric 2d-free fermions. Commun.Math. Phys. 105, 511–518 (1986). https://doi.org/10.1007/BF01238930
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DOI: https://doi.org/10.1007/BF01238930