Holomorphy, triality and non-perturbative beta function in 2d supersymmetric QCD

The constraints of N=2 supersymmetry, in combination with several other quite general assumptions, have recently been used to show that N=2 supersymmetric Yang-Mills theory has a low energy quantum parameter space symmetry characterised by the discrete group $\gu$. We show that if one also assumes the commutativity of renormalization group flow with the action of this group on the complexified coupling constant $\ta$, then this is sufficient to determine the non-perturbative ...

This article studies some features of quantum field theories with internal supersymmetry, focusing mainly on 2-dimensional non-linear sigma models which take values in a coset superspace. It is discussed how BRST operators from the target space supersymmetry algebra can be used to identify subsectors which are often simpler than the original model and may allow for an explicit computation of correlation functions. After an extensive discussion of the general reduction scheme,...

We derive the Wilsonian renormalization group equation in two dimensional ${\cal N}=2$ supersymmetric nonlinear sigma models. This equation shows that the sigma models on compact Einstein K\"{a}hler manifolds are aymptotically free. This result is gerenal and does not depend on the specific forms of the K\"{a}hler potentials. We also examine the renormalization group flow in a new model which connects two manifolds with different global symmetries.

Supersymmetric nonlinear sigma models have target spaces that carry interesting geometry. The geometry is richer the more supersymmetries the model has. The study of models with two dimensional world sheets is particularly rewarding since they allow for torsionful geometries. In this review I describe and exemplify the relation of $2d$ supersymmetry to Riemannian, complex, bihermitian, $(p,q)$ Hermitean, K\"ahler, hyperk\"ahler, generalised geometry and more

Beta-functions are derived for the flow of N=2 SUSY SU(2) Yang-Mills in 4-dimensions with massless matter multiplets in the fundamental representation of the gauge group. The beta-functions represent the flow of the couplings as the VEV of the Higgs field is lowered and are modular forms of weight -2. They have the correct asymptotic behaviour at both the strong and weak coupling fixed points. Corrections to the massless beta-functions when masses are turned on are discussed.

Classically integrable $\sigma$-models are known to be solutions of the 1-loop RG equations, or "Ricci flow", with only a few couplings running. In some of the simplest examples of integrable deformations we find that in order to preserve this property at 2 (and higher) loops the classical $\sigma$-model should be corrected by quantum counterterms. The pattern is similar to that of effective $\sigma$-models associated to gauged WZW theories. We consider in detail the examples...

The requirement that duality and renormalization group transformations commute as motions in the space of a theory has recently been explored to extract information about the renormalization flows in different statistical and field theoretical systems. After a review of what has been accomplished in the context of 2d sigma models, new results are presented which set up the stage for a fully generic calculation at two-loop order, with particular emphasis on the question of sch...

Motivated by the search for solvable string theories, we consider the problem of classifying the integrable bosonic 2d $\sigma$-models. We include non-conformal $\sigma$-models, which have historically been a good arena for discovering integrable models that were later generalized to Weyl-invariant ones. General $\sigma$-models feature a quantum RG flow, given by a 'generalized Ricci flow' of the target-space geometry. This thesis is based on the conjecture that integrable ...

The behavior of the beta-function of the low-energy effective coupling in the N=2 supersymmetric SU(2) QCD with several massive matter hypermultiplets and in the SU(3) Yang-Mills theory is determined near the superconformal points in the moduli space. The renormalization group flow is unambiguously fixed by looking at limited types of deformation near the superconformal points. It is pointed out that the scaling dimension of the beta-function is controlled by the scaling beha...

We construct a topological invariant of the renormalization group trajectories of a large class of 2D quantum integrable models, described by the thermodynamic Bethe ansatz approach. A geometrical description of this invariant in terms of triangulations of three-dimensional manifolds is proposed and associated dilogarithm identities are proven.