Twisted logarithmic modules of free field algebras

@article{Bakalov2016TwistedLM,
  title={Twisted logarithmic modules of free field algebras},
  author={Bojko Bakalov and McKay Sullivan},
  journal={arXiv: Quantum Algebra},
  year={2016}
}
Given a non-semisimple automorphism $\varphi$ of a vertex algebra $V$, the fields in a $\varphi$-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 $\beta\gamma$-system (even superfermions… 
Twisted Logarithmic Modules of Free Field and Lattice Vertex Algebras.
SULLIVAN, STEVEN MCKAY. Twisted Logarithmic Modules of Free Field and Lattice Vertex Algebras. (Under the direction of Bojko Bakalov.) Vertex algebras formalize the relations between vertex operators
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We construct two associative algebras from a vertex operator algebra $V$ and a general automorphism $g$ of $V$. The first, called $g$-twisted zero-mode algebra, is a subquotient of what we call
Twisted logarithmic modules of lattice vertex algebras
Twisted modules over vertex algebras formalize the relations among twisted vertex operators and have applications to conformal field theory and representation theory. A recent generalization, called
Logarithmic Vertex Algebras
We introduce and study the notion of a logarithmic vertex algebra, which is a vertex algebra with logarithmic singularities in the operator product expansion of quantum fields; thus providing a
Free Field Realisations in Logarithmic Conformal Field Theory
Invariances of conformal field theories (CFTs) would seem to suggest that correlation functions behave as power laws. However, logarithms also exhibit conformal invariance. When logarithms are
A Complete Bibliography of Publications in the Journal of Mathematical Physics: 2005{2009
(2 < p < 4) [200]. (Uq(∫u(1, 1)), oq1/2(2n)) [92]. 1 [273, 79, 304, 119]. 1 + 1 [252]. 2 [352, 318, 226, 40, 233, 157, 299, 60]. 2× 2 [185]. 3 [456, 363, 58, 18, 351]. ∗ [238]. 2 [277]. 3 [350]. p

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