Gauge invariants, correlators and holography in bosonic and fermionic tensor models

Koch, Robert de Mello; Gossman, David; Tribelhorn, Laila

doi:10.1007/jhep09(2017)011

Cited by 56 publications

(60 citation statements)

References 108 publications

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“…Indeed, some studies addressing the connection between the RMT properties of SYK and the OTOCs appeared in recent days: very recently, [58] has studied the onset of RMT behavior in the (Gaussian filtered) SYK SFF 6 and found that, in agreement with the results of [59], the time-scale at which the RMT behavior appears -which we will call Thouless time -is not the 4 Indeed, a priori there could be systems which are chaotic according to one definition and not chaotic according to the other. 5 For example, see the U (1) symmetry and flavor generalizations [16][17][18][19][20][21], supersymmetric generalizations [22][23][24][25][26][27], SYK(-like) models without disorder [28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43], gravity duals [44][45][46][47][48][49][50][51] and the Schwarzian theory [52][53][54]. 6 As we will revi...…”

Section: Introductionmentioning

confidence: 99%

The Thouless time for mass-deformed SYK

Nosaka¹,

Rosa²,

Yoon³

2018

J. High Energ. Phys.

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We study the onset of RMT dynamics in the mass-deformed SYK model (i.e., an SYK model deformed by a quadratic random interaction) in terms of the strength of the quadratic deformation. We use as chaos probes both the connected unfolded Spectral Form Factor (SFF) as well as the Gaussian-filtered SFF, which has been recently introduced in the literature. We show that they detect the chaotic/integrable transition of the massdeformed SYK model at different values of the mass deformation: the Gaussian-filtered SFF sees the transition for large values of the mass deformation; the connected unfolded SFF sees the transition at small values. The latter is in qualitative agreement with the transition as seen by the OTOCs. We argue that the chaotic/integrable deformation affect the energy levels inhomogeneously: for small values of the mass deformation only the lowlying states are modified while for large values of the mass deformation also the states in the bulk of the spectrum move to the integrable behavior. * nosaka@yukawa.kyoto-u.ac.jp † Dario85@kias.re.kr ‡ junggi.yoon@icts.res.in arXiv:1804.09934v1 [hep-th]

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Section: Introductionmentioning

confidence: 99%

The Thouless time for mass-deformed SYK

Nosaka¹,

Rosa²,

Yoon³

2018

J. High Energ. Phys.

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“…Both transform in the adjoint of U (N 3 ). Following [23] we can construct an exact collective description for T φ (2). We will extend the discussion of [23] by considering a model with a quartic potential.…”

Section: A "Planar Limit" For the Tensor Modelmentioning

confidence: 99%

“…The advantage of the restricted Schur polynomial basis follows because we are able, in the free theory, to compute correlators exactly. The results we will use are [23] O γ 1 γ 2…”

Section: Finite N Contributionsmentioning

confidence: 99%

Holography for tensor models

et al. 2020

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In this article we explore the holographic duals of tensor models using collective field theory. We develop a description of the gauge invariant variables of the tensor model. This is then used to develop a collective field theory description of the dynamics. We consider matrix like subsectors that develop an extra holographic dimension. In particular, we develop the collective field theory for the matrix like sector of an interacting tensor model. We check the correctness of the large N collective field by showing that it reproduces the perturbative expansion of large N expectation values. In contrast to this, we argue that melonic large N limits do not develop an extra dimension. This conclusion follows from the large N value for the melonic collective field, which has delta function support. The finite N physics of the model is also developed and non-perturbative effects in the 1/N expansion are exhibited. 1 robert@neo.phys.wits.ac.za 2

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“…The recent discovery of the relation between some sectors of Kronecker coefficients and Littlewood-Richardson numbers in the field of combinatorics and group theory. This is relevant for us since Kronecker coefficients organize the spectrum of eigenstates of free tensor models [29,30,31,32], whereas Littlewood-Richardson numbers have long been known to organize the spectrum of matrix models [34,35,36,37,38,39,40,41].…”

Section: Introductionmentioning

confidence: 99%

Tensor and matrix models: a one-night stand or a lifetime romance?

Díaz

2018

J. High Energ. Phys.

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The spectra of energy eigenstates of free tensor and matrix models are organized by Kronecker coefficients and Littlewood-Richardson numbers, respectively. Exploiting recent results in combinatorics for Kronecker coefficients, we derive a formula that relates Kronecker coefficients with a hook shape with Littlewood-Richardson numbers. This formula has a natural translation into physics: the eigenstates of the hook sector of tensor models are in one-to-one correspondence with fluctuations of 1/2-BPS states in multi-matrix models. We then conjecture the duality between both sectors. Finally, we study the Hagedorn behaviour of tensor models with finite rank of the symmetry group and, using similar arguments, suggest that the second (high energy) phase could be entirely described by multimatrix models.

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Gauge invariants, correlators and holography in bosonic and fermionic tensor models

Cited by 56 publications

References 108 publications

The Thouless time for mass-deformed SYK

The Thouless time for mass-deformed SYK

Holography for tensor models

Tensor and matrix models: a one-night stand or a lifetime romance?

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