Melonic theories over diverse number systems

Steven S. Gubser, Matthew Heydeman, Christian Jepsen, Sarthak Parikh, Ingmar Saberi, Bogdan Stoica, Brian Trundy

Research output: Contribution to journalArticle

10 Scopus citations


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.

Original languageEnglish (US)
Article number126007
JournalPhysical Review D
Issue number12
StatePublished - Dec 15 2018

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy (miscellaneous)

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    Gubser, S. S., Heydeman, M., Jepsen, C., Parikh, S., Saberi, I., Stoica, B., & Trundy, B. (2018). Melonic theories over diverse number systems. Physical Review D, 98(12), [126007].