Integrable deformed T1,1 sigma models from 4D Chern-Simons theory

• Published in: The journal of high energy physics Vol. 2021; no. 9
• Main Authors: Fukushima, Osamu, Sakamoto, Jun-ichi, Yoshida, Kentaroh
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 07.09.2021; Springer Nature B.V
• Subjects: Boundary conditions; Classical and Quantum Gravitation; Deformation; Elementary Particles; Field theory (physics); High energy physics; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Quantum theory; Regular Article - Theoretical Physics; Relativity Theory; String Theory; Two dimensional models; AdS-CFT Correspondence; Integrable Field Theories
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP09(2021)037

A bstract Recently, a variety of deformed T 1 , 1 manifolds, with which 2D non-linear sigma models (NLSMs) are classically integrable, have been presented by Arutyunov, Bassi and Lacroix (ABL) [ 46 ]. We refer to the NLSMs with the integrable deformed T 1 , 1 as the ABL model for brevity. Motivated by this progress, we consider deriving the ABL model from a 4D Chern-Simons (CS) theory with a meromorphic one-form with four double poles and six simple zeros. We specify boundary conditions in the CS theory that give rise to the ABL model and derive the sigma-model background with target-space metric and anti-symmetric two-form. Finally, we present two simple examples 1) an anisotropic T 1 , 1 model and 2) a G/H λ -model. The latter one can be seen as a one-parameter deformation of the Guadagnini-Martellini-Mintchev model.