Probing integrable perturbations of conformal theories using singular vectors

Pierre Mathieu; Gerard Watts

doi:10.1016/0550-3213(96)00325-2

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arXiv · hep-th/9603088

Probing integrable perturbations of conformal theories using singular vectors

Pierre Mathieu·Gerard Watts

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Abstract

It has been known for some time that the (1,3) perturbations of the (2k+1,2) Virasoro minimal models have conserved currents which are also singular vectors of the Virasoro algebra. This also turns out to hold for the (1,2) perturbation of the (3k+-1,3) models. In this paper we investigate the requirement that a perturbation of an extended conformal field theory has conserved currents which are also singular vectors. We consider conformal field theories with W3 and (bosonic) WBC2 = W(2,4) extended symmetries. Our analysis relies heavily on the general conjecture of de Vos and van Driel relating the multiplicities of W-algebra irreducible modules to the Kazhdan-Lusztig polynomials of a certain double coset. Granting this conjecture, the singular-vector argument provides a direct way of recovering all known integrable perturbations. However, W models bring a slight complication in that the conserved densities of some (1,2)-type perturbations are actually subsingular vectors, that is, they become singular vectors only in a quotient module.

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Pierre Mathieu, Gerard Watts. 1996-03-13. Probing integrable perturbations of conformal theories using singular vectors. https://doi.org/10.1016/0550-3213(96)00325-2

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