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.
Highlights
We refer to the NLSMs with the integrable deformed T 1,1 as the ABL model for brevity
We start from a certain meromorphic one-form with four double poles and six simple zeros
The first task is to find out a possible string-theory embedding of the ABL background
Summary
We shall consider 2D NLSMs with a family of deformed T 1,1 manifolds, which have been presented by Arutyunov-Bassi-Lacroix [46]. We will refer to them as the ABL model for brevity as explained in Introduction. Let us reproduce the ABL model from 4D CS theory. In the ABL model, the 2D surface M is embedded into the Lie group G × G. The twist function in (3.1) corresponds to the case with N = 2 and T = 2 in (3.14) in [46]. In specifying a 2D integrable model associated with ω, we need to choose a solution to the boundary equations of motion, αβ (Aα, ∂ξp Aα), δ(Aβ, ∂ξp Aβ) p = 0 , p ∈ p. The boundary equations of motion (3.3) take the same form as in the PCM with the WZ term case [23]. To derive the ABL model, we take the following solution:.
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