On $\beta$-function of $N=2$ supersymmetric integrable sigma-models

In this paper we consider perturbation theory in generic two-dimensional sigma models in the so-called first-order formalism, using the coordinate regularization approach. Our goal is to analyze the first-order formalism in application to $\beta$ functions and compare its results with the standard geometric calculations. Already in the second loop, we observe deviations from the geometric results that cannot be explained by the regularization/renormalization scheme choices. M...

We study regularization scheme dependence of $\beta$-function for sigma models with two-dimensional target space. Working within four-loop approximation, we conjecture the scheme in which the $\beta$-function retains only two tensor structures up to certain terms containing $\zeta_3$. Using this scheme, we provide explicit solutions to RG flow equation corresponding to Yang-Baxter- and $\lambda$-deformed $SU(2)/U(1)$ sigma models, for which these terms disappear.

We study the beta-function of the N=2 sigma-model coupled to N=2 induced supergravity. We compute corrections to first order in the semiclassical limit, $c \to -\infty$, beyond one-loop in the matter fields. As compared to the corresponding bosonic, metric sigma-model calculation, we find new types of contributions arising from the dilaton coupling automatically accounted for, once the K\"ahler potential is coupled to N=2 supergravity.

Following a suggestion made by Tseytlin, we investigate the case when one replaces the transverse part of the bosonic action by an $n=2$ supersymmetric sigma-model with a symmetric homogeneous K\"ahlerian target space. As conjectured by Tseytlin, the metric is shown to be exactly known since the beta function is known to reduce to its one-loop value.

We study renormalizable nonlinear sigma-models in two dimensions with N=2 supersymmetry described in superspace in terms of chiral and complex linear superfields. The geometrical structure of the underlying manifold is investigated and the one-loop divergent contribution to the effective action is computed. The condition of vanishing beta-function allows to identify a class of models which satisfy this requirement and possess N=4 supersymmetry.

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 w...

In this paper, we study the RG flow in the non-linear sigma models obtained from a 2d N=(0,2) supersymmetric QCD. The sigma model is parameterized by a single Kahler modulus. We determine its exact non-perturbative beta function using holomorphy, triality and the knowledge of the infra-red fixed point.

We discuss the dressing of one-loop sigma-model beta-functions by induced supergravity, for both N=1 and N=2 supersymmetric theories. We obtain exact results by a superconformal gauge argument, and verify them in the semi-classical limit by explicit perturbative calculations in the light-cone gauge. We find that for N=2 theories there is no dressing of the one-loop beta-functions.

We re-examine perturbative and nonperturbative aspects of the beta function in N=1 and N=2 supersymmetric gauge theories, make comments on the recent literature on the subject and discuss the exactness of several known results such as the NSVZ beta function.

We explain that the supersymmetric $CP^{n-1}$ sigma model is directly related to the level-zero chiral Gross-Neveu (cGN) model. In particular, beta functions of the two theories should coincide. This is consistent with the one-loop-exactness of the $CP^{n-1}$ beta function and a conjectured all-loop beta function of cGN models. We perform an explicit four-loop calculation on the cGN side and discuss the renormalization scheme dependence that arises.