Towards a quadratic Poisson algebra for the subtracted classical monodromy of symmetric space sine-Gordon theories

Delduc, F; Hoare, B; Magro, M

Abstract

Symmetric space sine-Gordon theories are two-dimensional massive integrable field theories, generalising the sine-Gordon and complex sine-Gordon theories. To study their integrability properties on the real line, it is necessary to introduce a subtracted monodromy matrix. Moreover, since the theories are not ultralocal, a regularisation is required to compute the Poisson algebra for the subtracted monodromy. In this article, we regularise and compute this Poisson algebra for certain configurations, and show that it can both satisfy the Jacobi identity and imply the existence of an infinite number of conserved quantities in involution.

Citation

Delduc, F., Hoare, B., & Magro, M. (2024). Towards a quadratic Poisson algebra for the subtracted classical monodromy of symmetric space sine-Gordon theories. Journal of Physics A: Mathematical and Theoretical, 57(6), Article 065401. https://doi.org/10.1088/1751-8121/ad1d91

• Journal Article Type: Article
• Acceptance Date: Jan 11, 2024
• Online Publication Date: Jan 29, 2024
• Publication Date: Feb 9, 2024
• Deposit Date: Feb 16, 2024
• Publicly Available Date: Feb 16, 2024
• Journal: Journal of Physics A: Mathematical and Theoretical
• Print ISSN: 1751-8113
• Electronic ISSN: 1751-8121
• Publisher: IOP Publishing
• Peer Reviewed: Peer Reviewed
• Volume: 57
• Issue: 6
• Article Number: 065401
• DOI: https://doi.org/10.1088/1751-8121/ad1d91
• Keywords: massive integrable 2D field theories, symmetric space sine-Gordon models, classical integrability, Poisson algebra
• Public URL: https://durham-repository.worktribe.com/output/2192692