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

Abstract

Abstract Recently, a variety of deformed T1,1 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 T1,1 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 T1,1 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.