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

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

1995-04-28

arxiv.org/abs/q-alg/9504026v1

Physics

High Energy Physics

High Energy Physics - Theory

40 pages, latex

Scientific paper

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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