Deformed $\sigma$-models, Ricci flow and Toda field theories

Abstract

It is shown that the Pohlmeyer map of a $\sigma$-model with a toric two-dimensional target space naturally leads to the `sausage' metric. We then elaborate the trigonometric deformation of the ${\mathrm{CP}}^{n-1}$-model, proving that its $T$-dual metric is Kähler and solves the Ricci flow equation. Finally, we discuss a relation between flag manifold $\sigma$-models and Toda field theories.

arXiv comment40 pages

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Cited by in corpus (5)

• 4-dimensional Chern-Simons theory and integrable field theories
• Flag manifold sigma models: spin chains and integrable theories
• Quantum flag manifold $\sigma$-models and Hermitian Ricci flow
• Geometric flow equations for the number of space-time dimensions
• $T\bar{T}$ Deformations in Curved Space from 4D Chern-Simons Theory