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2018

SYK-like tensor quantum mechanics with $\mathrm{Sp}(N)$ symmetry

Carrozza, Sylvain, Pozsgay, Victor

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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.

SYK-like tensor quantum mechanics with $\mathrm{Sp}(N)$ symmetry · Around

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