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

Abstract

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 multi-matrix models.

20 pages, 1 figure. References added

References in corpus (19)

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Cited by in corpus (14)

• On (q,t)-deformation of Gaussian matrix model
• Phases Of Melonic Quantum Mechanics
• From Kronecker to tableau pseudo-characters in tensor models
• Complete solution to Gaussian tensor model and its integrable properties
• Invariant Operators, Orthogonal Bases and Correlators in General Tensor Models
• An analogue of Schur functions for the plane partitions
• Tensorial generalization of characters
• Spontaneous Symmetry Breaking in Tensor Theories
• On generalized Macdonald polynomials
• Cut-and-join operators and Macdonald polynomials from the 3-Schur functions
• Holography for Tensor models
• Backgrounds from Tensor Models: A Proposal
• Chiral symmetry breaking generalizes in tensor theories
• The Non-melonic Sector of Tensor Models and Gravity