Abstract
We classify a large set of melonic theories with arbitrary q-fold interactions, demonstrating that the interaction vertices exhibit a range of symmetries, always of the form ℤ n2 for some n, which may be 0. The number of different theories proliferates quickly as q increases above 8 and is related to the problem of counting one-factorizations of complete graphs. The symmetries of the interaction vertex lead to an effective interaction strength that enters into the Schwinger-Dyson equation for the two-point function as well as the kernel used for constructing higher-point functions.
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Gubser, S.S., Jepsen, C., Ji, Z. et al. Higher melonic theories. J. High Energ. Phys. 2018, 49 (2018). https://doi.org/10.1007/JHEP09(2018)049
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DOI: https://doi.org/10.1007/JHEP09(2018)049