Recursion relations in p -adic Mellin Space
Abstract
In this work, we formulate a set of rules for writing down p -adic Mellin amplitudes at tree-level. The rules lead to closed-form expressions for Mellin amplitudes for arbitrary scalar bulk diagrams. The prescription is recursive in nature, with two different physical interpretations: one as a recursion on the number of internal lines in the diagram, and the other as reminiscent of on-shell BCFW recursion for flat-space amplitudes, especially when viewed in auxiliary momentum space. The prescriptions are proven in full generality, and their close connection with Feynman rules for real Mellin amplitudes is explained. We also show that the integrands in the Mellin–Barnes representation of both real and p -adic Mellin amplitudes, the so-called pre-amplitudes, can be constructed according to virtually identical rules, and that these pre-amplitudes themselves may be re-expressed as products of particular Mellin amplitudes with complexified conformal dimensions.
Additional Information
© 2019 IOP Publishing Ltd. Received 23 January 2019, revised 8 May 2019. Accepted for publication 17 May 2019. Published 17 June 2019. CBJ and SP thank Steven S Gubser, Matilde Marcolli, and Brian Trundy for useful discussions and encouragement. SP thanks the Perimeter Institute for their kind hospitality while this work was in progress. The work of CBJ was supported in part by the Department of Energy under Grant No. DE-FG02-91ER40671, by the US NSF under Grant No. PHY-1620059, and by the Simons Foundation, Grant 511167 (SSG). The work of SP was supported in part by Perimeter Institute for Theoretical Physics. Research at the Perimeter Institute is supported by the Government of Canada through the Department of Innovation, Science and Economic Development and by the Province of Ontario through the Ministry of Research, Innovation and Science.Attached Files
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Additional details
- Eprint ID
- 96466
- DOI
- 10.1088/1751-8121/ab227b
- Resolver ID
- CaltechAUTHORS:20190617-104718155
- DE-FG02-91ER40671
- Department of Energy (DOE)
- PHY-1620059
- NSF
- 511167
- Simons Foundation
- Perimeter Institute for Theoretical Physics
- Department of Innovation, Science and Economic Development (Canada)
- Ontario Ministry of Research, Innovation and Science
- Created
-
2019-06-17Created from EPrint's datestamp field
- Updated
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2022-07-12Created from EPrint's last_modified field