LAUSR

This is a proceedings based on the talk that was made in the workshop “Black Holes, Gravitational Waves and Spacetime Singularities” at Vatican Observatory on 9–12 May 2017. Since then we have constructed some corrections, hence this paper includes them. Here we employ the $$(1 + 1)$$(1+1)D Kitaev superconductor model and perform the Wilsonian renormalization group transformation in a real space. We regard the running energy scale or the repetition number of RG transformation as a new emergent direction of the spacetime, thus constructing a one dimensional higher spacetime. The solution for the beta function is plugged into the effective action and then the RG information is encoded in the curvature of the emergent spacetime. We found that there are two fixed points in which one corresponds to the Lifshitz spacetime with the dynamical critical exponent $$z=2$$z=2 and the other fixed point corresponds to the AdS$$_{3}$$3 spacetime. The topological superconducting phase induces a naked singularity in the spacetime and the trivial superconducting phase produces regular spacetime. Except the fixed points, each parameter phase shows spatial anisotropic spacetime description as it goes to IR limit.