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As in the question, can matrix model theory be generalized to a tensor model theory? Will the results be different or useful in describing real world phenomena?

Details: in matrix model theory we have an $N\times N$ matrix $M$ with the action given by $S=\dfrac 1g \int \text{tr} (M^2 +V(M) ) DM$, so can we replace $M= (M_{ij}) $ by $T_{ijk} $ for example, so that the free Lagrangian becomes $T_{ijk} T_{jik}$ or something alike?

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    $\begingroup$ There are several things that are called "matrix model". Please elaborate what exactly you mean here and how a generalization to "tensor model" is supposed to work (beyond merely replacing the word "matrix" with "tensor"). $\endgroup$ – ACuriousMind Jul 26 at 14:03
  • $\begingroup$ I have edited the question. $\endgroup$ – wilsonw Jul 26 at 14:19

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