1304.4152 (Valentin Bonzom et al.)

Fully packed loops on random surfaces and the 1/N expansion of tensor
models    [PDF]

Valentin Bonzom, Frédéric Combes

Starting with the observation that some fully packed loop models on random surfaces can be mapped to random edge-colored graphs, we show that the expansion in the number of loops is organized like the 1/N expansion of rank-three tensor models. In particular, configurations which maximize the number of loops are precisely the melonic graphs of tensor models and a scaling limit which projects onto the melonic sector is found. This also shows that some three-dimensional topologies can be obtained from discrete surfaces decorated with loops. We generalize this approach to higher-rank tensor models, for random tensors of size $N^{d-1} \times \tau N^{\beta}$ with beta between 0 and 1. They generate loops with fugacity $\tau N^\beta$ on triangulations in dimension d-1 and we show that the 1/N expansion is beta-dependent.

View original: http://arxiv.org/abs/1304.4152