O. Gamayun

A. Losev

M. Shifman

Inconsistencies between two approaches to deriving beta functions in two-dimensional sigma models are resolved by adding heavy superpartners.

Sigma models are important quantum field theories that describe mappings from the two-dimensional world sheet to target space. The beta functions of the first order formulation of Kähler sigma models can be derived in terms of the algebraic data of the theory or in terms of the geometry of their target space. We show how, by introducing extra heavy particles, the results of these two approaches can be reconciled.

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.

Peculiar betas tamed

First-order formalism for β functions in bosonic sigma models from supersymmetry breaking