Yang-Baxter Deformation of 2D Non-Linear Sigma Models: Towards Applications to AdS/CFT

The study of integrable systems, particularly non-perturbative techniques, has provided significant insight into real physics. This book focuses on classical integrability, which is well captured by the Arnold–Liouville theorem. Deformations preserving integrability have been developed, and a systematic method to perform integrable deformations of 2D non-linear sigma models was invented in 2002. Applications of Yang–Baxter deformation to string theory are also described.

Format: Paperback / softback
Length: 70 pages
Publication date: 04 June 2021
Publisher: Springer Verlag, Singapore

In the captivating realm of mathematical physics, the study of integrable systems stands as a fascinating topic of exploration. In particular, the development of non-perturbative techniques has yielded profound insights into the realm of real physics. There exist two fundamental notions of integrability: classical integrability and quantum integrability. Within this book, our focus lies on the former, classical integrability. When a system possesses a finite number of degrees of freedom, it has been elegantly captured by the renowned Arnold–Liouville theorem. However, when the number of degrees of freedom extends to infinity, as in classical field theories, the integrable structure undergoes a profound enrichment. In fact, the study of classically integrable field theories boasts a rich history, with various techniques, including the classical inverse scattering method, having been developed over the years. These techniques have been meticulously collected and well-documented in previously published books, readily accessible in traditional, standard textbooks.

One of the intriguing aspects of integrable systems is the investigation of deformations that preserve integrability. Typically, it is not considered a systematic approach to perform such deformations, necessitating a case-by-case study to demonstrate the integrability of deformed systems by constructing the associated Lax pair or action-angle variables.

Recently, a novel and systematic method to perform integrable deformations of 2D non-linear sigma models has emerged. This groundbreaking development was invented by C. Klimcik in 2002, and the integrability of the deformed sigma models was established in 2008. While the original work was initially focused on 2D principal chiral models, it has since been generalized in numerous directions.

In this book, we aim to present the recent progress on this Yang–Baxter deformation in a pedagogical manner, encompassing some simplifications to enhance understanding. By delving into the intricacies of this deformation, we hope to provide a comprehensive guide for those seeking to explore the fascinating world of classical integrable systems.

Weight: 454g
Dimension: 235 x 155 (mm)
ISBN-13: 9789811617027
Edition number: 1st ed. 2021