Random Tensors

Written by the creator of the modern theory of random tensors, this book is the first self-contained introductory text to this rapidly developing theory. Starting from notions familiar to the average researcher or PhD student in mathematical or theoretical physics, the book presents in detail the theory and its applications to physics.

The recent detections of the Higgs boson at the LHC and gravitational waves at LIGO mark new milestones in Physics confirming long standing predictions of Quantum Field Theory and General Relativity. These two experimental results only reinforce today the need to find an underlying common framework of the two: the elusive theory of Quantum Gravity.

Over the past thirty years, several alternatives have been proposed as theories of Quantum Gravity, chief among them String Theory. While these theories are yet to be tested experimentally, key lessons have already been learned. Whatever the theory of Quantum Gravity may be, it must incorporate random geometry in one form or another. This book introduces a framework for studying random geometries in any dimensions. Building on the resounding success of random matrices as theories of random two dimensional surfaces, random tensors are their natural generalization to theories of random geometry in arbitrary dimension. This book shows that many of the celebrated results in random matrices, most notably 't Hooft's 1/N expansion, can be generalized to higher dimensions. It provides a complete and self-contained derivation of the key results on random tensors.

Razvan Gheorghe Gurau, Researcher, Centre de Physique Theorique, Ecole Polytechnique, CNRS, Universite Paris-Saclay, France

Razvan Gurau studied as an undergraduate at the Physics Department of the University of Bucharest before coming to France in 2002 as an eleve of the Ecole Normale Superieure de Paris, Selection Internationale. He obtained his BA and MA degrees from the ENS and continued with a PhD in Mathematical Physics at the Universite Paris 11, graduating in 2008. From 2008 to 2012 he was a postdoctoral researcher and a senior postdoctoral researcher at the Perimeter Institute for Theoretical Physics. In 2012 he joined the Centre National de la Recherche Scientifique as a full-time researcher and obtained his Habilitation a diriger des recherches in 2015.