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Deformed $\sigma$-models, Ricci flow and Toda field theories
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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 K\"ahler and solves the Ricci flow equation. Finally, we discuss a relation between flag manifold $\sigma$-models and Toda field theories.
Forward citations
Cited by 2 Pith papers
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Anomalous symmetries in K\"ahler geometry
Every Kähler metric with a centrally extended Abelian isometry algebra is locally a quotient of a canonical model, and the anomalous isometries can be gauged using twisted chiral superfields.
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Nonperturbative features in the Lie-algebraic K\"ahler sigma model with fermions
In the deformed CP1 quantum mechanics with fermions, the nonperturbative ambiguity structure of the ground state energy persists, with the elongation parameter k conjectured to enter at three loops through g^4(k^2-1).
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