SYK-like tensor quantum mechanics with $\mathrm{Sp}(N)$ symmetry
| Autor: | Carrozza, Sylvain, Pozsgay, Victor |
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| Rok vydání: | 2018 |
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| Zdroj: | Nucl. Phys. B 941 (2019) 28-52 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.nuclphysb.2019.02.012 |
| Popis: | We introduce a family of tensor quantum-mechanical models based on irreducible rank-$3$ representations of $\mathrm{Sp}(N)$. In contrast to irreducible tensor models with $\mathrm{O}(N)$ symmetry, the fermionic tetrahedral interaction does not vanish and can therefore support a melonic large $N$ limit. The strongly-coupled regime has a very analogous structure as in the complex SYK model or in $\mathrm{U}(N)\times\mathrm{O}(N)\times\mathrm{U}(N)$ tensor quantum mechanics, the main difference being that the states are now singlets under $\mathrm{Sp}(N)$. We introduce character formulas that enumerate such singlets as a function of $N$, and compute their first values. We conclude with an explicit numerical diagonalization of the Hamiltonian in two simple examples: the symmetric model at $N=1$, and the antisymmetric traceless model at $N=3$. Comment: 24 pages, 5 figures, v2: minor improvements and references added, v3: matches published version |
| Databáze: | arXiv |
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