@article{93adc94c459f46e487483f2791b17c49,

title = "Melonic theories over diverse number systems",

abstract = "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.",

author = "Gubser, {Steven S.} and Matthew Heydeman and Christian Jepsen and Sarthak Parikh and Ingmar Saberi and Bogdan Stoica and Brian Trundy",

note = "Funding Information: 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. Funding Information: 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. Publisher Copyright: {\textcopyright} 2018 authors. Published by the American Physical Society.",

year = "2018",

month = dec,

day = "15",

doi = "10.1103/PhysRevD.98.126007",

language = "English (US)",

volume = "98",

journal = "Physical Review D",

issn = "2470-0010",

publisher = "American Physical Society",

number = "12",

}