The theory of physical superselection sectors in terms of vertex operator algebra language

Haisheng Li

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The theory of physical superselection sectors in terms of vertex operator algebra language

Haisheng Li

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Abstract

We formulate an interpretation of the theory of physical superselection sectors in terms of vertex operator algebra language. Using this formulation we give a construction of simple current from a primary semisimple element of weight one. We then prove that if a rational vertex operator algebra $V$ has a simple current $M$ satisfying certain conditions, then $V\oplus M$ has a natural rational vertex operator (super)algebra structure. Applying our results to a vertex operator algebra associated to an affine Lie algebra, we construct its simple currents and the extension by a simple current. We also present two essentially equivalent constructions for twisted modules for an inner automorphism from the adjoint module or any untwisted module.

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Haisheng Li. 1995-04-28. The theory of physical superselection sectors in terms of vertex operator algebra language. https://arxiv.org/abs/q-alg/9504026

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