Abstract
Tensor models generalize matrix models and generate colored triangulations of pseudo-manifolds in dimensions D ≥ 3. The free energies of some models have been recently shown to admit a double scaling limit, i.e. large tensor size N while tuning to criticality, which turns out to be summable in dimension less than six. This double scaling limit is here extended to arbitrary models. This is done by means of the Schwinger-Dyson equations, which generalize the loop equations of random matrix models, coupled to a double scale analysis of the cumulants.
Highlights
Controlled by the genus of the corresponding Feynman ribbon graphs
This is done by means of the Schwinger-Dyson equations, which generalize the loop equations of random matrix models, coupled to a double scale analysis of the cumulants
It is worth noticing that the double scaling limit in tensor models differs markedly from that in matrix models
Summary
Observables in random tensor theory are generalizations of trace-invariants in matrix models. Invariance requires all indices to be contracted It emerges that the generating polynomials can be labeled by connected, regular, bipartite graphs of degree D, whose edges have a color label drawn from {1, . D} such that the D edges incident to a vertex have distinct colors There are the 4-vertex bubbles illustrated in figure 1b D} is the color of the edges that, when cut, disconnect the graph Another (less important) example of a bubble is given in figure 1c.
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