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Higher-dimensional full vertex algebras and systems of conformally covariant correlation functions
Abstract
We formulate a class of systems of Euclidean correlation functions for compact d-dimensional conformal field theories which are not necessarily unitary. We also introduce conformal d-vertex algebras, d-dimensional analogues of full vertex algebras, and prove that such an algebra is obtained from every system of conformally covariant correlation functions. Finally, for each d≥ 2, we construct a family of examples satisfying these axioms, corresponding to generalized free scalar fields. For d>2, this family contains both unitary and non-unitary examples.
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BibTeX
@misc{moriwaki2026higherdimensional,
title = {{Higher-dimensional full vertex algebras and systems of conformally covariant correlation functions}},
author = {Yuto Moriwaki},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.37949},
eprint = {2609.37949},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.37949},
}
RIS
TY - UNPB
TI - Higher-dimensional full vertex algebras and systems of conformally covariant correlation functions
AU - Yuto Moriwaki
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.37949
UR - https://arxiv.org/abs/2609.37949
AB - We formulate a class of systems of Euclidean correlation functions for compact d-dimensional conformal field theories which are not necessarily unitary. We also introduce conformal d-vertex algebras, d-dimensional analogues of full vertex algebras, and prove that such an algebra is obtained from every system of conformally covariant correlation functions. Finally, for each d≥ 2, we construct a family of examples satisfying these axioms, corresponding to generalized free scalar fields. For d>2, this family contains both unitary and non-unitary examples.
ER -