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Logarithmic Intertwining Operators and Vertex Operators

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Abstract

This is the first in a series of papers where we study logarithmic intertwining operators for various vertex subalgebras of Heisenberg and lattice vertex algebras. In this paper we examine logarithmic intertwining operators associated with rank one Heisenberg vertex operator algebra M(1) a , of central charge 1 − 12a 2. We classify these operators in terms of depth and provide explicit constructions in all cases. Our intertwining operators resemble puncture operators appearing in quantum Liouville field theory. Furthermore, for a = 0 we focus on the vertex operator subalgebra L(1, 0) of M(1)0 and obtain logarithmic intertwining operators among indecomposable Virasoro algebra modules. In particular, we construct explicitly a family of hidden logarithmic intertwining operators, i.e., those that operate among two ordinary and one genuine logarithmic L(1, 0)-module.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University at Albany (SUNY), Albany, NY, 12222, USA

    Antun Milas

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  1. Antun Milas
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Correspondence to Antun Milas.

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Communicated by Y. Kawahigashi

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Milas, A. Logarithmic Intertwining Operators and Vertex Operators. Commun. Math. Phys. 277, 497–529 (2008). https://doi.org/10.1007/s00220-007-0375-3

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