Laplacians in polar matrix coordinates and radial fermionization in higher dimensions

Masuku, Mthokozisi; Rodrigues, J. P.

doi:10.1063/1.3553456

Cited by 13 publications

(15 citation statements)

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“…It is interesting to note that the formula for Ω(x, x ) is identical to the formula obtained from the radial sector of multi matrix models, and that the formula for ω(x) is very similar -see [78,79,80,81]. This easily leads to the following Hamiltonian (we have dropped constant terms)…”

Section: Collective Field Theorymentioning

confidence: 71%

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

Koch

Gossman

Tribelhorn

2017

J. High Energ. Phys.

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Motivated by the close connection of tensor models to the SYK model, we use representation theory to construct the complete set of gauge invariant observables for bosonic and fermionic tensor models. Correlation functions of the gauge invariant operators in the free theory are computed exactly. The gauge invariant operators close a ring. The structure constants of the ring are described explicitly. Finally, we construct a collective field theory description of the bosonic tensor model.

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Section: Collective Field Theorymentioning

confidence: 71%

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

Koch

Gossman

Tribelhorn

2017

J. High Energ. Phys.

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“…The formula for Ω(x, x ) coincides with the radial sector of multi matrix models and the formula for ω(x) is very similar -see[61,62,63,64].…”

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confidence: 71%

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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“…For an even number of hermitian matrices (or an arbitrary number of complex matrices) a closed sub sector 2 dependent on a single matrix only, that has properties expected of such radial matrix, has indeed been identified [4,5], and it is the purpose of this communication to discuss its large N dynamics.…”

Section: Jhep12(2015)035mentioning

confidence: 99%

“…with R hermitean and U unitary, R can be diagonalized as R = V † rV , with r a diagonal matrix and V unitary, we obtain [4,23] A ij…”

Section: Angular Degrees Of Freedommentioning

confidence: 99%

Large N matrix hyperspheres and the gauge-gravity correspondence

Masuku

Mulokwe

Rodrigues

2015

J. High Energ. Phys.

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Abstract:The large N dynamics of a subsector of d = 0 interacting complex multi matrix systems, which is naturally parametrized by a matrix valued radial coordinate, and which embodies the canonical AdS/CFT relationship between 't Hooft's coupling constant and radius, is obtained. Unlike the case of the single complex matrix, for two or more complex matrices a new repulsive logarithmic potential is present, and as a result the density of radial eigenvalues has support on an hyper annulus. For the single complex matrix, the integral over the angular degrees of freedom of the Yang-Mills interaction can be carried out exactly, and in the presence of an harmonic potential, the density of radial eigenvalues is shown to be of the Wigner type.

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Laplacians in polar matrix coordinates and radial fermionization in higher dimensions

Cited by 13 publications

References 50 publications

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

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

Holography for tensor models

Large N matrix hyperspheres and the gauge-gravity correspondence

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