# Reconstruction of a vertex algebra in higher dimensions from its one-dimensional restriction

@inproceedings{Bakalov2022ReconstructionOA, title={Reconstruction of a vertex algebra in higher dimensions from its one-dimensional restriction}, author={Bojko Bakalov and Nikolay M. Nikolov}, year={2022} }

. Vertex algebras in higher dimensions correspond to models of quantum ﬁeld theory with global conformal invariance. Any vertex algebra in higher dimensions admits a restriction to a vertex algebra in any lower dimension, and in particular, to dimension one. In this paper, we ﬁnd natural conditions under which the converse passage is possible. These conditions include a unitary action of the conformal Lie algebra with a positive energy, which is given by local endomorphisms and obeys certain…

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