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

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arxiv 2005.01812 v1 pith:JDEDTRR2 submitted 2020-05-04 hep-th math.DG

Dmitri Bykov , Dieter Lust This is my paper · ORCID
classification hep-thmath.DG
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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.

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  1. Nonperturbative features in the Lie-algebraic K\"ahler sigma model with fermions

    hep-th 2024-12 conditional novelty 6.0 of 10

    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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