Integrability using the Sine-Gordon and Thirring Duality

An introductory course

Alessandro Torrielli (University of Surrey)

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English

Institute of Physics Publishing
17 May 2024

Series: IOP ebooks

This book provides a detailed description of the duality between two integrable systems: the 1+1-dimensional Sine-Gordon model and the 1+1-dimensional Thirring model. While of great importance per se, this duality is only part of the target of the book. In order to reach an understanding of the subtleties involved in the duality, one has to take a journey through the properties of quantum integrable systems, building from the ground up the theory of exact S-matrices and familiarising oneself with the mathematical concept of a quantum group. The book therefore becomes an opportunity for a focussed study of integrability in its wider breadth of interest, always maintaining a clear ultimate purpose in mind: understanding the duality between bosons and fermions in 1+1 dimensions. This should make going through the book from the point of view of the reader/early-career researcher a live enterprise, as opposed to a more passive learning exercise.

Key Features:

The book fills a gap in the existing literature, collating a vast amount scattered literature, with uniformised notation and conventions The book’s format is ideal for use in PhD Schools and advanced graduate level mini courses, or for beginner PhD students as an introductory reference Originates for an invited set of lectures Contains a significant number of worked examples and problems, with solutions. It also presents several open-ended suggestions for literature reviews and guided learning through references

By: Alessandro Torrielli (University of Surrey)
Imprint: Institute of Physics Publishing
Country of Publication: United Kingdom
Dimensions: Height: 254mm, Width: 178mm,
ISBN: 9780750358972
ISBN 10: 0750358971
Series: IOP ebooks
Pages: 156
Publication Date: 17 May 2024
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

Preface Acknowledgements Author biography 1 Introduction 2 Invitation to integrable quantum field theories 3 The Sine-Gordon model 4 The Thirring model 5 Duality between Sine-Gordon and Thirring 6 Remarks on the duality 7 Supplement: the residue of the Lee-Yang model 8 Supplement: Hopf algebra properties 9 Supplement: Yangians 10 Supplement: the Lieb-Liniger model 11 Supplement: massless integrability 12 Supplement: a toy model for the Bethe ansatz

Alessandro Torrielli has been a member of staff at the University of Surrey since 2011, and appointed as Professor of Mathematics in 2022. He graduated with a 110/110 cum laude Laurea (equivalent to MSc) in Physics from Genoa University. He then undertook his PhD in Physics from Padua University, then held postdoctoral positions at Padua University, the Humboldt University of Berlin, the Massachusetts Institute of Technology MIT, Utrecht University and York University. His work focuses on algebraic aspects of integrable systems, in particular supersymmetric models of the type appearing in the AdS/CFT correspondence. His research papers have gathered 3867 citations to this day, and his current h-index is 30.