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arXiv · 2312.01885

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

Oleksandr Gamayun·Andrei Losev·Mikhail Shifman
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Abstract

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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Oleksandr Gamayun, Andrei Losev, Mikhail Shifman. 2023-12-04. First-order formalism for $\beta$ functions in bosonic sigma models from supersymmetry breaking. https://arxiv.org/abs/2312.01885

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