Abstract
We prove an orbifold conjecture for conformal field theory with a solvable automorphism group. Namely, we show that if V is a \({C_2}\) -cofinite simple vertex operator algebra and G is a finite solvable automorphism group of V, then the fixed point vertex operator subalgebra \({V^G}\) is also \({C_2}\) -cofinite, where \({C_2}\) -cofiniteness is equivalent to the condition that V has only finitely many isomorphism classes of simple V-modules (including weak modules) and all finitely generated V-modules have composition series. This result offers a mathematically rigorous background to orbifold theories with solvable automorphism groups.
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Communicated by Y. Kawahigashi
Supported by the Grants-in-Aids for Scientific Research, No. 22654002, The Ministry of Education, Science and Culture, Japan.
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Miyamoto, M. \({C_2}\) -Cofiniteness of Cyclic-Orbifold Models. Commun. Math. Phys. 335, 1279–1286 (2015). https://doi.org/10.1007/s00220-014-2252-1
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DOI: https://doi.org/10.1007/s00220-014-2252-1