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Infinite Family of Integrable Sigma Models Using Auxiliary Fields.

Christian Ferko1, Liam Smith2

  • 1Center for Quantum Mathematics and Physics (QMAP), Department of Physics &amp; Astronomy, <a href="https://ror.org/05rrcem69">University of California</a>, Davis, California 95616, USA.

Physical Review Letters
|October 11, 2024
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Summary
This summary is machine-generated.

We introduce a new class of 2D sigma models that are proven to be classically integrable. These models feature an auxiliary field mediating interactions and possess infinite conserved charges, including the principal chiral model.

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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.