Integrable Deformations of T-Dual σ Models

Area of Science:

• Theoretical Physics
• Mathematical Physics

Background:

• Two-dimensional sigma models are fundamental in theoretical physics, particularly in string theory and condensed matter.
• T-duality is a key concept in string theory, relating different string theories.
• Classical integrability is a crucial property for exactly solvable models.

Purpose of the Study:

• To present a novel method for deforming T duals of two-dimensional sigma models.
• To ensure the preservation of classical integrability in the deformed models.
• To generalize existing deformation techniques like Yang-Baxter deformations.

Main Methods:

• Introducing a linear operator "ω" acting on the dualized subalgebra.
• Ensuring the operator "ω" satisfies the 2-cocycle condition.
• Utilizing field redefinitions to establish equivalences between models.

Main Results:

• A method to deform (generically non-Abelian) T duals of 2D sigma models while preserving classical integrability.
• Identification of deformed models by a linear operator "ω" satisfying the 2-cocycle condition.
• Proof of equivalence between homogeneous Yang-Baxter deformations and the proposed deformed models for invertible "ω".

Conclusions:

• The presented method provides a unified framework for deforming T duals of sigma models.
• The findings offer new insights into the structure and properties of integrable field theories.
• The generalization to supercoset models expands the applicability of the method.