Integrable deformed $T^{1,1}$ sigma models from 4D Chern-Simons theory

Abstract

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) [arXiv:2010.05573]. 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 $G/H$ $\lambda$-model. The latter one can be seen as a one-parameter deformation of the Guadagnini-Martellini-Mintchev model.

23 pages: minor modifications, references added

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Cited by in corpus (5)

• 4-dimensional Chern-Simons theory and integrable field theories
• Non-Abelian Toda field theories from a 4D Chern-Simons theory
• 4D Chern-Simons theory with auxiliary fields
• The Courant-Hilbert construction in 4D Chern-Simons theory
• 3-dimensional mixed BF theory and Hitchin's integrable system