Mukherjee, J (2021) Partition functions of higher derivative conformal fields on conformally related spaces. In: Journal of High Energy Physics, 2021 (10).
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Abstract
The character integral representation of one loop partition functions is useful to establish the relation between partition functions of conformal fields on Weyl equivalent spaces. The Euclidean space Sa � AdSb can be mapped to Sa+b provided Sa and AdSb are of the same radius. As an example, to begin with, we show that the partition function in the character integral representation of conformally coupled free scalars and fermions are identical on Sa � AdSb and Sa+b. We then demonstrate that the partition function of higher derivative conformal scalars and fermions are also the same on hyperbolic cylinders and branched spheres. The partition function of the four-derivative conformal vector gauge field on the branched sphere in d = 6 dimension can be expressed as an integral over �naive� bulk and �naive� edge characters. However, the partition function of the conformal vector gauge field on Sq1 � AdS5 contains only the �naive� bulk part of the partition function. This follows the same pattern which was observed for the partition of conformal p-form fields on hyperbolic cylinders. We use the partition function of higher derivative conformal fields on hyperbolic cylinders to obtain a linear relationship between the Hofman-Maldacena variables which enables us to show that these theories are non-unitary. © 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 Springer Science and Business Media Deutschland GmbH |
| Department/Centre: | Division of Physical & Mathematical Sciences > Centre for High Energy Physics |
| Date Deposited: | 25 Nov 2021 04:43 |
| Last Modified: | 25 Nov 2021 04:43 |
| URI: | http://eprints.iisc.ac.in/id/eprint/70499 |
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