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

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.