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First-order formalism for $\beta$ functions in bosonic sigma models from supersymmetry breaking

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arxiv 2312.01885 v1 pith:LAR5WVJM submitted 2023-12-04 hep-th cond-mat.stat-mechmath-phmath.MP

Oleksandr Gamayun , Andrei Losev , Mikhail Shifman This is my paper · ORCID
classification hep-thcond-mat.stat-mechmath-phmath.MP
keywords first-ordermodelssigmabetacurrent-currentdeformationsformalismfunctions
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We consider the renormalization group flow equation for the two-dimensional sigma models with the K\"ahler target space. The first-order formulation allows us to treat perturbations in these models as current-current deformations. We demonstrate, however, that the conventional first-order formalism misses certain anomalies in the measure, and should be amended. We reconcile beta functions obtained within the conformal perturbation theory for the current-current deformations with traditional ``geometric" results obtained in the background field methods, in this way resolving the peculiarities pointed out in [JHEP10(2023)097]. The result is achieved by the supersymmetric completion of the first-order sigma model.

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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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