Outline

Integrable field theories have applications in various areas of physics, such as high-energy physics, condensed matter, and mathematics. In this introductory 4-class course, a general overview of the subject will be provided. We will begin with the notion of integrability in classical mechanical systems and field theories, highlighting its relationship with the existence of conserved charges. Next, we will explore the consequences of these conserved charges in quantum field theories, emphasizing integrability’s constraints on the theory’s scattering matrix. We will also discuss integrability in spin chains and their solution through the Bethe Ansatz. Finally, we will consider how these ideas apply to the study of scaling dimensions in conformal gauge theories in 4 dimensions.

Resources

References

• Dorey, Patrick. “Exact S-matrices.” Conformal Field Theories and Integrable Models: Lectures Held at the Eötvös Graduate Course, Budapest, Hungary, 13–18 August 1996. Berlin, Heidelberg: Springer Berlin Heidelberg, 2007. 85-125.- arXiv
• Z. Bajnok “How Integrability Works (for AdS/CFT)”.-InspireHep
• Faddeev, L. D. (1996). “How algebraic Bethe ansatz works for integrable model”.- arXiv