Universal critical behavior in tensor models for four-dimensional quantum gravity
Astrid Eichhorn (CP3-Origins, University of Southern Denmark, Campusvej 55, Odense M, DK-5230, Denmark, Institute for Theoretical Physics, University of Heidelberg, Philosophenweg 16, Heidelberg, 69120, Germany); Johannes Lumma (Institute for Theoretical Physics, University of Heidelberg, Philosophenweg 16, Heidelberg, 69120, Germany); Antonio Pereira (Instituto de Física, Universidade Federal Fluminense, Campus da Praia Vermelha, Av. Litorânea s/n, Niterói, RJ, 24210-346, Brazil, Physics Department, Quaid-i-Azam University, Islamabad, 45320, Pakistan); Arslan Sikandar (Institute for Theoretical Physics, University of Heidelberg, Philosophenweg 16, Heidelberg, 69120, Germany, Physics Department, Quaid-i-Azam University, Islamabad, 45320, Pakistan)
Four-dimensional random geometries can be generated by statistical models with rank-4 tensors as random variables. These are dual to discrete building blocks of random geometries. We discover a potential candidate for a continuum limit in such a model by employing background-independent coarse-graining techniques where the tensor size serves as a pre-geometric notion of scale. A fixed point candidate which features two relevant directions is found. The possible relevance of this result in view of universal results for quantum gravity and a potential connection to the asymptotic-safety program is discussed.