Quantum chaos and holographic tensor models

By Chethan Krishnan, Sambuddha Sanyal, P. N. Bala Subramanian. Journal of High Energy Physics, 2016

182 citations recorded by the source corpus.

A class of tensor models were recently outlined as potentially calculable examples of holography: their perturbative large-N behavior is similar to the Sachdev-Ye-Kitaev (SYK) model, but they are fully quantum mechanical (in the sense that there is no quenched disorder averaging). These facts make them intriguing tentative models for quantum black holes. In this note, we explicitly diagonalize the simplest non-trivial Gurau-Witten tensor model and study its spectral and late-time properties. We find parallels to (a single sample of) SYK where some of these features were recently attributed to random matrix behavior and quantum chaos. In particular, the spectral form factor exhibits a dip-ramp-plateau structure after a running time average, in qualitative agreement with SYK. But we also observe that even though the spectrum has a unique ground state, it has a huge (quasi-?)degeneracy of intermediate energy states, not seen in SYK. If one ignores the delta function due to the degeneracies however, there is level repulsion in the unfolded spacing distribution hinting chaos. Furthermore, there are gaps in the spectrum. The system also has a spectral mirror symmetry which we trace back to the presence of a unitary operator with which the Hamiltonian anticommutes. We use it to argue that to the extent that the model exhibits random matrix behavior, it is controlled not by the Dyson ensembles, but by the BDI (chiral orthogonal) class in the Altland-Zirnbauer classification.

Subfields: Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/7a134a2db424b01d788ad8502b1224f20eb2e5cf

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In Atomic and Molecular Physics, and Optics

1. Rifath Khan
2. Chethan Krishnan
3. Sanchita Sharma

In Nuclear and High Energy Physics

1. Rifath Khan
2. Chethan Krishnan
3. Sanchita Sharma

In Statistical and Nonlinear Physics

1. Rifath Khan
2. Chethan Krishnan
3. Sanchita Sharma

Citations in the corpus

• Circuit complexity in fermionic field theory (2018, background): “These theories are not field theories, but they offer the possibility of exact solvability [14], and therefore it might be possible to calculate complexity for them exactly.”