Symmetry breaking

Abstract

AbstractFor the quartic tensor models, the critical point at which the continuum limit is reached corresponds to a phase transition accompanied by a symmetry breaking. This chapter analyzes a simplified quartic tensor model for which the vacuum state in the broken phase can be identified. For this simplified model a genuinely new geometric phase in double scaling is obtained. The phase transition is a phase transition between a phase of planar surfaces and a phase of planar nodal surfaces. The emergent geometry obtained (in double scaling) is not yet genuinely D-dimensional, but, very likely, it is a Brownian sphere. However, this is a first step in the quest for a genuinely new random geometry in higher dimensions: for the first time a non-branched polymer state of higher dimensional random geometry is found in a scaling regime of tensor models.