Special Issue on Tensor Models, Formalism and Applications
The Guest Editor for this special issue is
Matrix models are a very successful framework for the study of random surfaces, instrumental in string theory, quantum gravity in dimension 2, conformal field theory, integrability, etc. However,the generalization of matrix models to higher dimensions has been a thorny issue for a long time. The first generalizations of matrix models, known as tensor models and group field theories, date back to 1990. However, for a long time progress has been slow, mainly due to the lack of an equivalent of the famous $1/N$ expansion of matrix models in higher dimensions. This problem has been solved in 2010 when the $1/N$ expansion for tensor models has been found. Since then, the field underwent a tremendous transformation and numerous results on tensor models, tensor field theories and group field theories have been established.
Today, tensor models provide a well defined and analytically controlled framework for the study of random geometries in higher dimension with possible applications to statistical physics in random geometry, conformal field theory and quantum gravity. This issue will bring together a collection of up to date reviews on the various aspects of the modern theory of tensor models. It's purpose is to serve as a reference for both mathematical and theoretical physicists, covering an in depth presentation of the mathematical formalism and its applications.
The issue contains 9 papers with the total of 264 pages.
We would like to thank all the authors who have published papers in the issue, and to give our special thanks to all the referees for providing constructive reviews.
Papers in this Issue: