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

Díaz, Pablo

doi:10.1007/jhep06(2018)140

Cited by 12 publications

(11 citation statements)

References 89 publications

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“…Strong interest in melonic theories, mostly fermionic quantum models, has been rekindled in recent times by the Sachdev-Ye-Kitaev (SYK) model [2,6] and various generalizations thereof [7,8], see also [9] and the review [10]. Within a program that has seen the convergence of very diverse approaches, new and interesting relations have been found between condensed-matter disordered systems [11][12][13][14], tensor models [15][16][17] and random matrix theory [18,19]. The emerging general picture is that melonic theories provide a quantum mechanical description of the near-horizon, low energy limit of near-extremal black holes [6,9].…”

Section: Introduction and Discussionmentioning

confidence: 99%

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Phases of melonic quantum mechanics

Ferrari

Massolo

2019

Phys. Rev. D

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We explore in detail properties of two melonic quantum mechanical theories which can be formulated either as fermionic matrix quantum mechanics in the new large D limit, or as disordered models. Both models have a mass parameter m and the transition from the perturbative large m region to the strongly coupled "black-hole" small m region is associated with several interesting phenomena. One model, with UðnÞ 2 symmetry and equivalent to complex Sachdev-Ye-Kitaev, has a line of first-order phase transitions terminating, for a strictly positive temperature, at a critical point having nontrivial, nonmean-field critical exponents for standard thermodynamical quantities. Quasinormal frequencies, as well as Lyapunov exponents associated with out-of-time-ordered four-point functions, are also singular at the critical point, leading to interesting new critical exponents. The other model, with reduced UðnÞ symmetry, has a quantum critical point at strictly zero temperature and positive critical mass m Ã . For 0 < m < m Ã , it flows to a new gapless IR fixed point, for which the standard scale invariance is spontaneously broken by the appearance of distinct scaling dimensions Δ þ and Δ − for the Euclidean two-point function when t → þ∞ and t → −∞ respectively. We provide several detailed and pedagogical derivations, including rigorous proofs or simplified arguments for some results that were already known in the literature.

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Section: Introduction and Discussionmentioning

confidence: 99%

“…The last condition above follows from time-reversal invariance, which is always valid in the leading large N melonic limit we are interested in. 19 It is natural to decompose ϕ into a disconnected and a connected piece,…”

Section: General Definitions and Propertiesmentioning

confidence: 99%

Phases of melonic quantum mechanics

Ferrari

Massolo

2019

Phys. Rev. D

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“…We therefore expect that finite rank tensor models offer a dual description of a brane system, at least at the some energy regime. We intend to report our progress into this direction in forthcoming [63] and future works.…”

Section: Summary and Future Workmentioning

confidence: 99%

“…Our idea is to utilize the mathematical fact that Kronecker coefficients (which are known to have a higher degree of complexity than Littlewood-Richardson numbers [60]) are actually expressible as LR numbers for specific cases [61,62]. These cases precisely label the specific states belonging to the energy regime n ∼ N, where both phases of the tensor model start to coexist [63]. We therefore expect that finite rank tensor models offer a dual description of a brane system, at least at the some energy regime.…”

Section: Summary and Future Workmentioning

confidence: 99%

Invariant operators, orthogonal bases and correlators in general tensor models

Díaz

Rey

2018

Nuclear Physics B

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We study invariant operators in general tensor models. We show that representation theory provides an efficient framework to count and classify invariants in tensor models of (gauge) symmetry G d = U (N 1 ) ⊗ · · · ⊗ U (N d ). As a continuation and completion of our earlier work, we present two natural ways of counting invariants, one for arbitrary G d and another valid for large rank of G d . We construct bases of invariant operators based on the counting, and compute correlators of their elements. The basis associated with finite rank of G d diagonalizes the two-point function of the free theory. It is analogous to the restricted Schur basis used in matrix models. We show that the constructions get almost identical as we swap the Littlewood-Richardson numbers in multi-matrix models with Kronecker coefficients in general tensor models. We explore the parallelism between matrix model and tensor model in depth from the perspective of representation theory and comment on several ideas for future investigation. *

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“…In what follows we will simply state and use the results we need. The reader requiring more details is encouraged to consult [59,23], as well as [83,84,85,86].…”

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

Cited by 12 publications

References 89 publications

Phases of melonic quantum mechanics

Phases of melonic quantum mechanics

Invariant operators, orthogonal bases and correlators in general tensor models

Holography for tensor models

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