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arXiv · 1806.04800

Higher melonic theories

Steven S. Gubser·Christian Jepsen·Ziming Ji·Brian Trundy
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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 $\mathbb{Z}_2^n$ 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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Steven S. Gubser, Christian Jepsen, Ziming Ji, Brian Trundy. 2018-06-12. Higher melonic theories. https://doi.org/10.1007/jhep09(2018)049

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