Non-Abelian Toda field theories from a 4D Chern-Simons theory

Abstract

We derive non-abelian Toda field theories (NATFTs) from a 4d Chern-Simons (CS) theory with two order defects by employing a certain asymptotic boundary condition. The 4d CS theory is characterized by a meromorphic 1-form $\omega$\,. We adopt $\omega$ with two simple poles and no zeros, and each of the order defects is located at each pole. As a result, an anisotropy parameter ${\beta }^2$ can be identified with the distance between the two defects. As examples, we can derive the (complex) sine-Gordon model and the Liouville theory.

23 pages

References in corpus (8)

• Pohlmeyer reduction of AdS_5 x S^5 superstring sigma model
• Dyonic Giant Magnons
• Pohlmeyer reduction revisited
• The Chern-Simons Origin of Superstring Integrability
• Yang-Baxter deformations of the Principal Chiral Model plus Wess-Zumino term
• On the Zakharov-Mikhailov action: $4$d Chern-Simons origin and covariant Poisson algebra of the Lax connection
• The Faddeev-Reshetikhin model from a 4D Chern-Simons theory
• Integrable deformed $T^{1,1}$ sigma models from 4D Chern-Simons theory

Cited by in corpus (5)

• 4D Chern-Simons theory with auxiliary fields
• Higher Gauge Theory and Integrability
• Gauging The Diamond: Integrable Coset Models from Twistor Space
• The Courant-Hilbert construction in 4D Chern-Simons theory
• 3-dimensional mixed BF theory and Hitchin's integrable system