Permutation-twisted modules for even order cycles acting on tensor product vertex operator superalgebras - INSPIRE

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Permutation-twisted modules for even order cycles acting on tensor product vertex operator superalgebras

Oct 14, 2013

35 pages

Published in:

Int.J.Math. 25 (2014) 1450018

Published: 2014

e-Print:

1310.3812 [math.QA]

DOI:

10.1142/S0129167X14500189

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Abstract: (arXiv)

We construct and classify

(1 \; 2 \; \cdots \; k)

-twisted

V^{\otimes k}

-modules for

k

even and

V

a vertex operator superalgebra. In particular, we show that the category of weak

(1 \; 2 \; \cdots \; k)

-twisted

V^{\otimes k}

-modules for

k

even is isomorphic to the category of weak parity-twisted

V

-modules. This result shows that in the case of a cyclic permutation of even order, the construction and classification of permutation-twisted modules for tensor product vertex operator superalgebras is fundamentally different than in the case of a cyclic permutation of odd order, as previously constructed and classified by the first author. In particular, in the even order case it is the parity-twisted

V

-modules that play the significant role in place of the untwisted

V

-modules that play the significant role in the odd order case.

Note:

arXiv admin note: text overlap with arXiv:math/9803118, arXiv:1310.1956. Constant term in Corollary 6.5 corrected; other minor typos corrected; reference to arXiv:1401.4635 added; minor clarifications in exposition made. To appear in the International Journal of Mathematics

Vertex operator superalgebras
twisted sectors
permutation orbifold
superconformal field theory
supersymmetry: algebra
category
cyclic
algebra: vertex
field theory: conformal

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