Infinite Family of Integrable Sigma Models Using Auxiliary Fields

Area of Science:

• Theoretical Physics
• Mathematical Physics
• Quantum Field Theory

Background:

• Sigma models are fundamental in theoretical physics, particularly in quantum field theory and string theory.
• Integrability is a key property in many physical systems, simplifying their analysis and revealing deep structures.

Purpose of the Study:

• To introduce and analyze a novel family of two-dimensional (2D) sigma models.
• To demonstrate the classical integrability of these models and their relation to known theories.

Main Methods:

• Parametrization of 2D sigma models using a function of one variable.
• Inclusion of an auxiliary field to mediate interactions.
• Construction of conserved charges from a Lax representation for the equations of motion.

Main Results:

• Every theory within this family is proven to be classically integrable.
• An infinite set of conserved charges in involution has been identified.
• The class encompasses the principal chiral model (PCM) and its deformations.

Conclusions:

• The introduced class of 2D sigma models offers a unified framework for studying integrable systems.
• The findings provide new insights into the mathematical structures underlying quantum field theories.
• This work establishes a connection between sigma models, integrability, and conserved quantities.