Uncolored random tensors, melon diagrams, and the Sachdev-Ye-Kitaev models
By I. Klebanov, G. Tarnopolsky. 2016
360 citations recorded by the source corpus.
Certain models with rank-$3$ tensor degrees of freedom have been shown by Gurau and collaborators to possess a novel large $N$ limit, where $g^2 N^3$ is held fixed. In this limit the perturbative expansion in the quartic coupling constant, $g$, is dominated by a special class of "melon" diagrams. We study "uncolored" models of this type, which contain a single copy of real rank-$3$ tensor. Its three indexes are distinguishable; therefore, the models possess $O(N)^3$ symmetry with the tensor field transforming in the tri-fundamental representation. Such uncolored models also possess the large $N$ limit dominated by the melon diagrams. The quantum mechanics of a real anti-commuting tensor therefore has a similar large $N$ limit to the model recently introduced by Witten as an implementation of the Sachdev-Ye-Kitaev (SYK) model which does not require disorder. Gauging the $O(N)^3$ symmetry in our quantum mechanical model removes the non-singlet states; therefore, one can search for its well-defined gravity dual. We point out, however, that the model possesses a vast number of gauge-invariant operators involving higher powers of the tensor field, suggesting that the complete gravity dual will be intricate. We also discuss the quantum mechanics of a complex 3-index anti-commuting tensor, which has $U(N)^2\times O(N)$ symmetry and argue that it is equivalent in the large $N$ limit to a version of SYK model with complex fermions. Finally, we discuss similar models of a commuting tensor in dimension $d$. While the quartic interaction is not positive definite, we construct the large $N$ Schwinger-Dyson equation for the two-point function and show that its solution is consistent with conformal invariance. We carry out a perturbative check of this result using the $4-\epsilon$ expansion.
Subfields: Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/e0d048afe3cba79790f0fe6389de8b32bf4f5f9f
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Citations in the corpus
- Notes on the complex Sachdev-Ye-Kitaev model (2019, neutral): “)(2 h ) (2)(2 1)sin(2ˇ) sin(ˇh sin(2ˇ sin(2ˇ) sin( ˇh) (B.1) is symmetric, and therefore, the eigenvectors of K G(h) = W (h)W G(h) are v 1 = 1 1 T and v 2 = 1 1 T with eigenvalues denoted as kA=S [6,50,51] K G(h)v 1 = kA(h)v 1 ; kA(h) = (2 h)(2 + h 1) (2 2)(2 + 1) 1 sin(ˇh) sin(2ˇ) ; (B.2) K G(h”
- Fermionic localization of the schwarzian theory (2017, background): “@ ˝g)2]. The partition function for such a particle was already known to be one-loop exact [27]. One expects this theory to be relevant at low-energies for generalizations of SYK with global symmetry [28, 29, 30, 31]. 3.3 Super-Virasoro We can get an interesting generalization by considering super-V”
- Circuit complexity in fermionic field theory (2018, background): “In particular, one possible case where a strongly coupled gauge theory could be solvable is in the context of the so-called SYK-like tensor models [15].”
- The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual (2017, background): “ the thermodynamics is more conveniently described using the density of states [25]: e F = Z= Z ˆ(E)e EdE; ˆ(E) /es 0Nsinh 2ˇ p 2N S(E E 0)=J : (19) Variants of the SYK model have been studied in [29,30,31,32,33,34,35]. 1.1 Outline of the paper Let J˛1 and let us consider all quantities in the N!1”
- An introduction to the SYK model (2018, methodology): “, and [97] for an earlier string inspired model. Supersymmetry has so far been important in the construction of SYK models in higher dimensions [44], unless perhaps one works in non-integer dimension [98,18], see also [99{ 13 Figure 6: A lattice of SYK \quantum dots", with quartic all-to-all in”
- The quantum gravity dynamics of near extremal black holes (2018, positive): “Another application of our result is to connect with SYK type models [31, 32, 33, 34] since those models all have an emergent Schwarzian action at low energy.”
- The Schwarzian theory — origins (2018, methodology): “ional 2d CFT, as in e.g. [75]. These theories also seem to be related to group eld theories, utilized in the spinfoam formulation of LQG, which in turn seem to be related to the tensor models of e.g. [76, 77]. A very interesting extension to study deeper would be to understand N= 2 Liouville theory ”