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On deformation theory of quantum vertex algebras

Harald Grosse·Karl-Georg Schlesinger
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Abstract

We study an algebraic deformation problem which captures the data of the general deformation problem for a quantum vertex algebra. We derive a system of coupled equations which is the counterpart of the Maurer-Cartan equation on the usual Hochschild complex of an assocative algebra. We show that this system of equations results from an action principle. This might be the starting point for a perturbative treatment of the deformation problem of quantum vertex algebras. Our action generalizes the action of the Kodaira-Spencer theory of gravity and might therefore also be of relevance for applications in string theory.

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Harald Grosse, Karl-Georg Schlesinger. 2005-08-30. On deformation theory of quantum vertex algebras. https://arxiv.org/abs/hep-th/0508225

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