Double scaling in tensor models with a quartic interaction

作者：Dartois Stephane^*; Gurau Razvan; Rivasseau Vincent

来源：The Journal of High Energy Physics, 2013, 2013(9): 088.

DOI：10.1007/JHEP09(2013)088

• Matrix Models
• 1/N Expansion
• Models of Quantum Gravity

In this paper we identify and analyze in detail the subleading contributions in the 1/N expansion of random tensors, in the simple case of a quartically interacting model. The leading order for this 1/N expansion is made of graphs, called melons, which are dual to particular triangulations of the D-dimensional sphere, closely related to the %26quot;stacked%26quot; triangulations. For D %26lt; 6 the subleading behavior is governed by a larger family of graphs, hereafter called cherry trees, which are also dual to the D-dimensional sphere. They can be resummed explicitly through a double scaling limit. In sharp contrast with random matrix models, this double scaling limit is stable. Apart from its unexpected upper critical dimension 6, it displays a singularity at fixed distance from the origin and is clearly the first step in a richer set of yet to be discovered multi-scaling limits.

• 出版日期2013-9-17