Higher melonic theories

Journal of High Energy Physics, Sep 2018

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 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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Higher melonic theories

Journal of High Energy Physics September 2018, 2018:49 | Cite as Higher melonic theories AuthorsAuthors and affiliations Steven S. GubserChristian JepsenZiming JiBrian Trundy Open Access Regular Article - Theoretical Physics First Online: 10 September 2018 26 Downloads 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 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. Keywords 1/N Expansion Conformal Field Theory Nonperturbative Effects  ArXiv ePrint: 1806.04800 Download to read the full article text Notes Open Access This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. References [1] V. Bonzom, R. Gurau, A. Riello and V. Rivasseau, Critical behavior of colored tensor models in the large N limit, Nucl. Phys. B 853 (2011) 174 [arXiv:1105.3122] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar [2] R. Gurau and J.P. Ryan, Colored tensor models — A review, SIGMA 8 (2012) 020 [arXiv:1109.4812] [INSPIRE].MathSciNetzbMATHGoogle Scholar [3] S. Carrozza and A. Tanasa, O(N) random tensor models, Lett. Math. Phys. 106 (2016) 1531 [arXiv:1512.06718] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar [4] E. Witten, An SYK-like model without disorder, arXiv:1610.09758 [INSPIRE]. [5] I.R. Klebanov and G. Tarnopolsky, Uncolored random tensors, melon diagrams and the Sachdev-Ye-Kitaev models, Phys. Rev. D 95 (2017) 046004 [arXiv:1611.08915] [INSPIRE].ADSMathSciNetGoogle Scholar [6] S. Sachdev and J. Ye, Gapless spin fluid ground state in a random, quantum Heisenberg magnet, Phys. Rev. Lett. 70 (1993) 3339 [cond-mat/9212030] [INSPIRE]. [7] A. Kitaev, A simple model of quantum holography, talks given at KITP, April 7 and May 27 (2015).Google Scholar [8] P. Narayan and J. Yoon, SYK-like tensor models on the lattice, JHEP 08 (2017) 083 [arXiv:1705.01554] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar [9] S. Choudhury et al., Notes on melonic O(N)q − 1 tensor models, JHEP 06 (2018) 094 [arXiv:1707.09352] [INSPIRE].ADSCrossRefGoogle Scholar [10] F. Ferrari, V. Rivasseau and G. Valette, A new large N expansion for general matrix-tensor models, arXiv:1709.07366 [INSPIRE]. [11] G. Tarnopolsky, On large q expansion in the Sachdev-Ye-Kitaev model, arXiv:1801.06871 [INSPIRE]. [12] C. Jepsen, Adelic tensor models, Princeton University Pre-thesis, Princeton U.S.A. (2017).Google Scholar [13] L.E. Dickson and F.H. Safford, Solution to problem 8 (group theory), Amer. Math. Month. 13 (1906) 150.MathSciNetCrossRefGoogle Scholar [14] E.N. Gelling, On one-factorizations of a complete graph and the relationship to round-robin schedules, Ph.D. thesis, University of Victoria, Victoria, Canada (1973).Google Scholar [15] E.N. Gelling and R.E. Odeh, On 1-factorizations of a complete graph and the relationship to round-robin schedules, Congr. Numer. 9 (1974) 213.MathSciNetzbMATHGoogle Scholar [16] J.H. Dinitz and D.R. Stinson, A hill-climbing algorithm for the construction of one-factorizations and Room squares, SIAM J. Alg. Discr. Meth. 8 (1987) 430.MathSciNetCrossRefzbMATHGoogle Scholar [17] E. Seah and D.R. Stinson, On the enumeration of one-factorizations of complete graphs containing prescribed automorphism groups, Math. Comput. 50 (1988) 607.MathSciNetCrossRefzbMATHGoogle Scholar [18] J.H. Dinitz, D.K. Garnick and B.D. McKay, There are 526,915,620 nonisomorphic one-factorizations of K12, J. Comb. Designs 2 (1994) 273.CrossRefzbMATHGoogle Scholar [19] P. Kaski and P. R. Östergard, There are 1,132,835,421,602,062,347 nonisomorphic one-factorizations of K14, J. Comb. Designs 17 (2009) 147.CrossRefzbMATHGoogle Scholar [20] S.S. Gubser et al., Signs of the time: melonic theories over diverse number systems, arXiv:1707.01087 [INSPIRE]. [21] K. Bulycheva, I.R. Klebanov, A. Milekhin and G. Tarnopolsky, Spectra of Operators in Large N Tensor Models, Phys. Rev. D 97 (2018) 026016 [arXiv:1707.09347] [INSPIRE].ADSGoogle Scholar [22] I.R. Klebanov, A. Milekhin, F. Popov and G. Tarnopolsky, Spectra of eigenstates in fermionic tensor quantum mechanics, Phys. Rev. D 97 (2018) 106023 [arXiv:1802.10263] [INSPIRE].ADSGoogle Scholar [23] P.J. Cameron, Parallelisms of complete designs, London Mathematical Society Lecture Note Series, Cambridge University Press, Cambridge U.K. (976).Google Scholar [24] J. Polchins (...truncated)


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Steven S. Gubser, Christian Jepsen, Ziming Ji, Brian Trundy. Higher melonic theories, Journal of High Energy Physics, 2018, pp. 49, Volume 2018, Issue 9, DOI: 10.1007/JHEP09(2018)049