Causal tensor models for 4d Lorentzian quantum gravity and their phase structure via functional renormalization

• Applicant: Dr. Andreas Georg Aristides Pithis
• Subject Area: Nuclear and Elementary Particle Physics, Quantum Mechanics, Relativity, Fields
• Term: since 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 527121685

A central problem for elementary physics is the development of a theory of quantum gravitation. The tensor model (TM) approach attacks this by studying discrete random geometries in d-dimensions. Therein, rank-d tensors correspond to d-dimensional geometric building blocks. The action encodes how to stick them together to form extended triangulations. Hence, TMs generalize matrix models for 2d quantum gravity and are firmly linked to Causal Dynamical Triangulations (CDT) and Group Field Theory (GFT). Their main challenge is to recover well-defined continuum geometries like our spacetime. For a recent class of TMs, Gurau et al. found that triangulations of d-dimensional spheres dominate their 1/N-expansion, with N denoting the size of the tensor. Regrettably, this still leads to pathological geometries in the continuum limit. This evidently indicates that additional structure is needed to recover d-dimensional continuum geometries from TMs. Extraordinarily, CDT shows that one can yield such geometries with de Sitter-like characteristics if one enforces global or local causality conditions onto its components. Recently, together with collaborators I succeeded to introduce conditions analogous to the global ones in a rank-4 TM for Lorentzian quantum gravity in 4d. The first objective of my project is thus to go beyond this by imposing causality conditions locally therein to yield a second model. To scrutinize if these two models can escape the sector of pathological geometries, one has to study their continuum limits. The suitable instrument for this is provided by the compelling and well-defined Functional Renormalization Group (FRG) method which is also applicable to TMs and GFTs. Thus, my second objective is to employ this method to chart the phase structure of these new and causal TMs and then to compare the results. I expect that they can yield phases corresponding to extended semiclassical geometries. This would be a considerable discovery for the TM approach and generally for quantum gravity research.

• DFG Programme: Research Grants