Random Tensors

Hardcover | November 5, 2016

byRazvan Gheorghe Gurau

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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 detailthe 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 frameworkof 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 incorporaterandom 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 randomgeometry 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.

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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 detailthe theory and its applications to physics....

Randazvan Gheorghe Gurandau 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 Universi...
Format:HardcoverDimensions:352 pages, 9.69 × 6.73 × 0.98 inPublished:November 5, 2016Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0198787936

ISBN - 13:9780198787938

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Table of Contents

1. Introduction2. Preliminaries3. Generalities on edge colored graphs4. The classification of edge colored graphs5. Melonic graphs6. The universality theorem7. A digest of matrix models8. The perturbative expansion of tensor models9. The quartic tensor model10. The double scaling limit11. Symmetry breaking12. ConclusionsAppendices