Orthogonal bases of invariants in tensor models

Díaz, Pablo; Rey, Soo‐Jong

doi:10.1007/jhep02(2018)089

Cited by 30 publications

(29 citation statements)

References 57 publications

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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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“…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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“…Each invariant is associated with the specific way indices of Φ and indices of Φ are contracted subjected to a double coset equivalence, see [42] for details. Counting the number of invariant operators, building a basis which diagonalizes the two-point function of the free theory and computing correlators has been a recent subject of study [29,33,30,31,32]. In those studies it was manifest the prominent role of Kronecker coefficients in organizing the spectrum of energy eigenstates.…”

Section: Tensor Partition Functionmentioning

confidence: 99%

“…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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“…Some of the insights come from the Virasoro structure of the matrix models [27][28][29][30][31][32][33][34] and its combinatorics and finding its counterpart in tensor models in general is expected to pave the way to bring progress in this field. Recent references include [35][36][37][38][39][40][41][42][43][44][45][46][47][48].…”

Section: Introductionmentioning

confidence: 99%

Generalized cut operation associated with higher order variation in tensor models

Itoyama

Yoshioka

2019

Nuclear Physics B

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The cut and join operations play important roles in tensor models in general. We introduce a generalization of the cut operation associated with the higher order variations and demonstrate how they generate operators in the Aristotelian tensor model. We point out that, by successive choices of appropriate variations, the cut operation generalized this way can generate those operators which do not appear in the ring of the join operation, providing a tool to enumerate the operators by a level by level analysis recursively. We present a set of rules that control the emergence of such operators. *

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Orthogonal bases of invariants in tensor models

Cited by 30 publications

References 57 publications

Holography for tensor models

Holography for tensor models

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

Generalized cut operation associated with higher order variation in tensor models

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