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Kac-Moody algebras, conformal symmetry and critical exponents. (English) Zbl 0661.17014

A group-theoretical method is presented for constructing new unitary representations of the Virasoro algebra out of Fermi fields. Some of these commute with Kac-Moody algebras constructed out of the Fermi fields (via the “quark model”) and some have a supersymmetric extension. An example with both these properties is relevant to the tricritical Ising model at the critical temperature. The critical exponents are calculated explicitly from the construction.

MSC:

17B65 Infinite-dimensional Lie (super)algebras
17B67 Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras
81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations
22E70 Applications of Lie groups to the sciences; explicit representations
82B26 Phase transitions (general) in equilibrium statistical mechanics
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References:

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