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arXiv · 1604.00375

Twisted logarithmic modules of free field algebras

Bojko Bakalov·McKay Sullivan
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Abstract

Given a non-semisimple automorphism $φ$ of a vertex algebra $V$, the fields in a $φ$-twisted $V$-module involve the logarithm of the formal variable, and the action of the Virasoro operator $L_0$ on such module is not semisimple. We construct examples of such modules and realize them explicitly as Fock spaces when $V$ is generated by free fields. Specifically, we consider the cases of symplectic fermions (odd superbosons), free fermions, and $βγ$-system (even superfermions). In each case, we determine the action of the Virasoro algebra.

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BibTeXRIS

Bojko Bakalov, McKay Sullivan. 2016-06-16. Twisted logarithmic modules of free field algebras. https://doi.org/10.1063/1.4953249

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