2023/12/04 by Gamayun, Oleksandr, Losev, Andrei, Shifman, Mikhail
#FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Statistical Mechanics (cond-mat.stat-mech)
paper · doi:10.48550/arxiv.2312.01885
We consider the renormalization group flow equation for the two-dimensional sigma models with the Kähler 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.