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Melonic theories over diverse number systems

Gubser, Steven S. and Heydeman, Matthew and Jepsen, Christian and Parikh, Sarthak and Saberi, Ingmar and Stoica, Bogdan and Trundy, Brian (2018) Melonic theories over diverse number systems. Physical Review D, 98 (12). Art. No. 126007. ISSN 2470-0010. doi:10.1103/PhysRevD.98.126007.

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Melonic field theories are defined over the p-adic numbers with the help of a sign character. Our construction works over the reals as well as the p-adics, and it includes the fermionic and bosonic Klebanov-Tarnopolsky models as special cases; depending on the sign character, the symmetry group of the field theory can be either orthogonal or symplectic. Analysis of the Schwinger-Dyson equation for the two-point function in the leading melonic limit shows that power law scaling behavior in the infrared arises for fermionic theories when the sign character is non-trivial, and for bosonic theories when the sign character is trivial. In certain cases, the Schwinger-Dyson equation can be solved exactly using a quartic polynomial equation, and the solution interpolates between the ultraviolet scaling controlled by the spectral parameter and the universal infrared scaling. As a by-product of our analysis, we see that melonic field theories defined over the real numbers can be modified by replacing the time derivative by a bilocal kinetic term with a continuously variable spectral parameter. The infrared scaling of the resulting two-point function is universal, independent of the spectral parameter of the ultraviolet theory.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Heydeman, Matthew0000-0001-7033-9075
Jepsen, Christian0000-0002-1159-0574
Parikh, Sarthak0000-0002-5831-3873
Alternate Title:Signs of the time: Melonic theories over diverse number systems
Additional Information:© 2018 Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3. Received 7 August 2018; published 13 December 2018. We thank M. Marcolli and P. Witaszczyk for extensive discussions. B. S. would also like to thank A. Almheiri for useful discussions. The work of S. S. G., C. J., S. P. and B. T. was supported in part by the Department of Energy under Grant No. DE-FG02-91ER40671. The work of S. P. was also supported in part by the Bershadsky Family Fellowship Fund in Mathematics or Physics. The work of M. H. was supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632 as well as by the Walter Burke Institute for Theoretical Physics at Caltech. The work of B. S. was supported in part by the Simons Foundation, and by the U.S. Department of Energy under Grant No. DE-SC-0009987. B. S. would like to thank the Stanford Institute for Theoretical Physics at Stanford University and the Aspen Center for Physics for hospitality. The work of B. S. was performed in part at Aspen Center for Physics, which is supported by National Science Foundation Grant No. PHY-1607611.
Group:Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Department of Energy (DOE)DE-FG02-91ER40671
Bershadsky Family Fellowship FundUNSPECIFIED
Department of Energy (DOE)DE-SC0011632
Walter Burke Institute for Theoretical Physics, CaltechUNSPECIFIED
Simons FoundationUNSPECIFIED
Department of Energy (DOE)DE-SC-0009987
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Issue or Number:12
Record Number:CaltechAUTHORS:20170707-115445821
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:78855
Deposited By: Joy Painter
Deposited On:07 Jul 2017 20:12
Last Modified:15 Nov 2021 17:43

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