### 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.

Original language | English (US) |
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Article number | 126007 |

Journal | Physical Review D |

Volume | 98 |

Issue number | 12 |

DOIs | |

State | Published - Dec 15 2018 |

### All Science Journal Classification (ASJC) codes

- Physics and Astronomy (miscellaneous)

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## Cite this

*Physical Review D*,

*98*(12), [126007]. https://doi.org/10.1103/PhysRevD.98.126007