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Complete Solution of a Gauged Tensor Model · Around

2018

Complete Solution of a Gauged Tensor Model

Krishnan, Chethan, Kumar, K. V. Pavan

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Building on a strategy introduced in arXiv:1706.05364, we present exact analytic expressions for all the singlet eigenstates and eigenvalues of the simplest non-linear ($n=2, d=3$) gauged Gurau-Witten tensor model.

This solves the theory completely.
The ground state eigenvalue is $-2\sqrt{14}$ in suitable conventions.
This matches the result obtained for the ground state energy in the ungauged model, via brute force diagonalization on a computer.

Built on

R. Gurau, “Invitation to Random Tensors,” SIGMA 12
Original
2011
Earlier work this paper cites.
S. Sachdev and J. Ye, “Gapless spin fluid ground state in a random, quantum Heisenberg magnet,” Phys. Rev. Lett. 70
Original
2015
Earlier work this paper cites.
J. Polchinski and V. Rosenhaus, “The Spectrum in the Sachdev-Ye-Kitaev Model,” JHEP 1604
Original
2016
Earlier work this paper cites.
J. Maldacena and D. Stanford, “Remarks on the Sachdev-Ye-Kitaev model,” Phys. Rev. D 94
Original
2016
Earlier work this paper cites.
R. M. Soni and S. P. Trivedi, “Aspects of Entanglement Entropy for Gauge Theories,” JHEP 1601
Original
2016
Earlier work this paper cites.

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2017

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E. Witten, “An SYK-Like Model Without Disorder,” arXiv:1610.09758 [hep-th]

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S. Choudhury, A. Dey, I. Halder, L. Janagal, S. Minwalla and R. Poojary, “Notes on Melonic O ( N ) q − 1 O(N)^{q-1} Tensor Models,” arXiv:1707.09352 [hep-th]

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I. R. Klebanov, A. Milekhin, F. Popov and G. Tarnopolsky, “On the Spectra of Eigenstates in Fermionic Tensor Quantum Mechanics,” arXiv:1802.10263 [hep-th]

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C. Krishnan, K. V. Pavan Kumar and P. N. Bala Subramanian, “(Anti-)Symmetrizing Wave Functions,” arXiv:1711.09811 [hep-th]

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J. Sonner and M. Vielma, “Eigenstate thermalization in the Sachdev-Ye-Kitaev model,” arXiv:1707.08013 [hep-th];

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2018

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