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Partition functions of p-forms from Harish-Chandra characters

David, JR and Mukherjee, J (2021) Partition functions of p-forms from Harish-Chandra characters. In: Journal of High Energy Physics, 2021 (9).

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Official URL: https://doi.org/10.1007/JHEP09(2021)094


We show that the determinant of the co-exact p-form on spheres and anti-de Sitter spaces can be written as an integral transform of bulk and edge Harish-Chandra characters. The edge character of a co-exact p-form contains characters of anti-symmetric tensors of rank lower to p all the way to the zero-form. Using this result we evaluate the partition function of p-forms and demonstrate that they obey known properties under Hodge duality. We show that the partition function of conformal forms in even d + 1 dimensions, on hyperbolic cylinders can be written as integral transforms involving only the bulk characters. This supports earlier observations that entanglement entropy evaluated using partition functions on hyperbolic cylinders do not contain contributions from the edge modes. For conformal coupled scalars we demonstrate that the character integral representation of the free energy on hyperbolic cylinders and branched spheres coincide. Finally we propose a character integral representation for the partition function of p-forms on branched spheres. © 2021, The Author(s).

Item Type: Journal Article
Publication: Journal of High Energy Physics
Publisher: Springer Science and Business Media Deutschland GmbH
Additional Information: The copyright for this article belongs to Authors
Department/Centre: Division of Physical & Mathematical Sciences > Centre for High Energy Physics
Date Deposited: 03 Dec 2021 08:39
Last Modified: 03 Dec 2021 08:39
URI: http://eprints.iisc.ac.in/id/eprint/70254

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