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A new view of the virasoro algebra

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Abstract

It is shown that the local quantum field theory of the chiral energy-momentum tensor with central chargec = 1 coincides with the gauge invariant subtheory of the chiral SU(2) current algebra at level 1, where the gauge group is the global SU(2) symmetry. At higher level, the same scheme gives rise toW-algebra extensions of the Virasoro algebra.

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References

  1. Buchholz, D. and Schulz-Mirbach, H., Haag duality in conformal quantum field theory,Rev. Math. Phys. 2, 105 (1990).

    Google Scholar 

  2. Langerholc, J. and Schroer, B., Can current operators determine a complete theory?Comm. Math. Phys. 4, 123 (1967).

    Google Scholar 

  3. Kac, V. G., Infinite-dimensional Lie algebras and Dedekind'sη-function,Funct. Anal. Appl. 8, 68 (1974).

    Google Scholar 

  4. Pressley, A. and Segal, G.,Loop Groups, Oxford Univ. Press, Oxford, 1986.

    Google Scholar 

  5. Kac, V. G.,Infinite Dimensional Lie Algebras, Birkhauser Verlag, Basel, 1983; Fuchs, J.,Affine Lie Algebras and Quantum Groups, Cambridge Univ. Press, Cambridge, 1992.

    Google Scholar 

  6. Segal, G., Unitary representations of some infinite dimensional groups,Comm. Math. Phys. 80, 301 (1981).

    Google Scholar 

  7. Kac, V. G., Contravariant form for the infinite dimensional Lie algebras and superalgebras, in W. Beiglböcket al. (eds)Group Theoretical Methods in Physics, Lecture Notes in Phys. 94, Springer-Verlag, New York, 1979, p. 441.

    Google Scholar 

  8. Doplicher, S., Haag, R., and Roberts, J. E., Fields, observables, and gauge transformations.I, Comm. Math. Phys. 13, 1 (1969); Local observables and particle statistics.I, Comm. Math. Phys. 23, 199 (1971).

    Google Scholar 

  9. Bais, F. A., Bouwknegt, P., Surridge, M., and Schoutens, K., Extensions of the Virasoro algebra constructed from Kac-Moody algebras using higher order Casimir invariants,Nuclear Phys. B 304, 348 (1988).

    Google Scholar 

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  1. II. Inst. Theor. Physik, Univ. Hamburg, D-22761, Hamburg, Germany

    Karl -Henning Rehren

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  1. Karl -Henning Rehren
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Rehren, K.H. A new view of the virasoro algebra. Lett Math Phys 30, 125–130 (1994). https://doi.org/10.1007/BF00939700

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