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

For various two dimensional non linear $\sigma$ models, we present a direct comparison between the $\beta$ functions computed with the $2+\epsilon$ renormalization group and the $\beta$ functions measured by Monte Carlo simulations. The theoretical and measured $\beta$ functions match each other nicely for models with a trivial topology, yet they disagree clearly for models containing topological defects. In these later cases, they are compatible with a phase transition at a ...

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.

The off-shell description of N=(2,2) supersymmetric non-linear sigma-models is reviewed. The conditions for ultra-violet finiteness are derived and T-duality is discussed in detail.

We construct a family of holomorphic $\beta$-functions whose RG flow preserves the $\Gamma(2)$ modular symmetry and reproduces the observed stability of the Hall plateaus. The semi-circle law relating the longitudinal and Hall conductivities that has been observed experimentally is obtained from the integration of the RG equations for any permitted transition which can be identified from the selection rules encoded in the flow diagram. The generic scale dependance of the cond...

An algebraic proof of the nonrenormalization theorem for the perturbative beta function of the coupling constant of N=2 Super Yang-Mills theory is provided. The proof relies on a fundamental relationship between the N=2 Yang-Mills action and the local gauge invariant polynomial Tr phi^2, phi(x) being the scalar field of the N=2 vector gauge multiplet. The nonrenormalization theorem for the beta function follows from the vanishing of the anomalous dimension of Tr phi^2.

We construct supersymmetric conformal sigma models in three dimensions. Nonlinear sigma models in three dimensions are nonrenormalizable in perturbation theory. We use the Wilsonian renormalization group equation method, which is one of the nonperturbative methods, to find the fixed points. Existence of fixed points is extremely important in this approach to show the renormalizability. Conformal sigma models are defined as the fixed point theories of the Wilsonian renormaliza...

We discuss the ultra-violet properties of bosonic and supersymmetric noncommutative non-linear sigma-models in two dimensions, both with and without a Wess-Zumino-Witten term.

We consider a general N=(2,2) non-linear sigma-model in (2,2) superspace. Depending on the details of the complex structures involved, an off-shell description can be given in terms of chiral, twisted chiral and semi-chiral superfields. Using superspace techniques, we derive the conditions the potential has to satisfy in order to be ultra-violet finite at one loop. We pay particular attention to the effects due to the presence of semi-chiral superfields. A complete descriptio...

We analyse with the algebraic, regularisation independant, cohomological B.R.S. methods, the renormalisability of torsionless N=2 and N= 4 supersymmetric non-linear $\si$ models built on K\"ahler spaces. Surprisingly enough with respect to the common wisdom, in the case of N=2 supersymmetry, we obtain an anomaly candidate, at least in the compact K\"ahler Ricci-flat case. If its coefficient does differ from zero, such anomaly would imply the breaking of global N=2 supersymmet...

Two-dimensional field theories do not have a moduli space of vacua. Instead, it is common that their low-energy behavior is a sigma model with a target space. When this target space is compact its renormalization group flow is standard. When it is non-compact the continuous spectrum of operators can change the qualitative behavior. Here we discuss two-dimensional gauge theories with N=(2,2) supersymmetry. We focus on two specific theories, for which we argue that they flow to...