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Exact Solution of a Strongly Coupled Gauge Theory in 0+1 Dimensions · Around

2018

Exact Solution of a Strongly Coupled Gauge Theory in 0+1 Dimensions

Krishnan, Chethan, Kumar, K. V. Pavan

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Gauged tensor models are a class of strongly coupled quantum mechanical theories.

We present the exact analytic solution of a specific example of such a theory: namely the smallest colored tensor model due to Gurau and Witten that exhibits non-linearities.
We find explicit analytic expressions for the eigenvalues and eigenstates, and the former agree precisely with previous numerical results on (a subset of) eigenvalues of the ungauged theory.
The physics of the spectrum, despite the smallness of $N$, exhibits rudimentary signatures of chaos.

Built on

R. Gurau, “Invitation to Random Tensors,” SIGMA 12
Original
2016
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2016
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J. Maldacena and D. Stanford, “Remarks on the Sachdev-Ye-Kitaev model,” Phys. Rev. D 94
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2016
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V. Bonzom, L. Lionni and A. Tanasa, “Diagrammatics of a colored SYK model and of an SYK-like tensor model, leading and next-to-leading orders,” J. Math. Phys. 58
Original
2017
Earlier work this paper cites.

Similar

J. Murugan, D. Stanford and E. Witten, “More on Supersymmetric and 2d Analogs of the SYK Model,” JHEP 1708
Original
2017
Cited alongside, same era.
J. S. Cotler et al
Original
2017
Cited alongside, same era.
C. Krishnan, K. V. P. Kumar and S. Sanyal, “Random Matrices and Holographic Tensor Models,” JHEP 1706
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2017
Cited alongside, same era.
C. Krishnan, S. Sanyal and P. N. Bala Subramanian, “Quantum Chaos and Holographic Tensor Models,” JHEP 1703
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2017
Cited alongside, same era.
E. Witten, “An SYK-Like Model Without Disorder,” arXiv:1610.09758 [hep-th]
Original
Cited in the paper.
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];
Original
Cited in the paper.
C. Krishnan and K. V. Pavan Kumar, “Complete Solution of a Gauged Tensor Model,” arXiv:1804.10103 [hep-th]
Original
Cited in the paper.
S. Chaudhuri, V. I. Giraldo-Rivera, A. Joseph, R. Loganayagam and J. Yoon, “Abelian Tensor Models on the Lattice,” arXiv:1705.01930 [hep-th];
Original
Cited in the paper.
C. Krishnan, K. V. P. Kumar and A. Raju, To Appear
Cited in the paper.

Then

C. Krishnan and K. V. P. Kumar, “Towards a Finite- N N Hologram,” JHEP 1710
Original
2017
Later among the works it cites.
I. R. Klebanov and G. Tarnopolsky, “Uncolored random tensors, melon diagrams, and the Sachdev-Ye-Kitaev models,” Phys. Rev. D 95
Original
2017
Later among the works it cites.
C. Krishnan, K. V. Pavan Kumar and D. Rosa, “Contrasting SYK-like Models,” JHEP 1801
Original
2018
Closest in time.
T. Nosaka, D. Rosa and J. Yoon, “The Thouless time for mass-deformed SYK,” JHEP 1809
Original
2018
Closest in time.

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