Related papers: Beta Function, C--Theorem and WDVV Equations in 4D…
We say that a function F(tau) obeys WDVV equations, if for a given invertible symmetric matrix eta^{alpha beta} and all tau \in T \subset R^n, the expressions c^{alpha}_{beta gamma}(tau) = eta^{alpha lambda} c_{lambda beta gamma}(tau) =…
We claim that if by a choice of the couplings the theory can be made conformally invariant (vanishing of the beta functions) it is automatically finite and vice versa. This is demonstrated by explicit example in supersymmetric gauge theory.…
The NSVZ $\beta$ functions in two-dimensional $\mathcal N=(0,2)$ supersymmetric models are revisited. We construct and discuss a broad class of such models using the gauge formulation. All of them represent direct analogs of…
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…
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…
We discuss the long-distance physics of 2d adjoint QCD when it is viewed as an effective field theory, and determine the beta functions for its two classically-marginal four-fermi operators. These four-fermion terms preserve the invertible…
We consider two-dimensional $\mathcal{N}=(0,2)$ sigma models with the CP(1) target space. A minimal model of this type has one left-handed fermion. Nonminimal extensions contain, in addition, $N_f$ right-handed fermions. Our task is to…
We propose an all orders beta function for ordinary Yang-Mills theories with or without fermions inspired by the Novikov-Shifman-Vainshtein-Zakharov beta function of N=1 supersymmetric gauge theories. The beta function allows us to bound…
We study regularization scheme dependence of K\"ahler ($N=2$) supersymmetric sigma models. At the one-loop order the metric $\beta$ function is the same as in non-supersymmetric case and coincides with the Ricci tensor. First correction in…
In this note we show that $\beta'_*$, the $\beta$-function slopes in the electric and magnetic theories are equal at the corresponding infrared fixed points. This follows from the scaling of the correlators of the trace of the energy…
We study discrete (duality) symmetries of functional determinants. An exact transformation of the effective action under the inversion of background fields $\beta (x) \to \beta^{-1}(x)$ is found. We show that in many cases this inversion…
The perturbative $\beta$-function is known exactly in a number of supersymmetric theories and in the 't Hooft renormalization scheme in the $\phi_4^4$ model. It is shown how this allows one to compute the effective action exactly for…
We propose and prove a trinomial version of the celebrated Bailey's lemma. As an application we obtain new fermionic representations for characters of some unitary as well as nonunitary models of N = 2 superconformal field theory (SCFT). We…
We prove that a $4d$ theory of non-linear electrodynamics has equations of motion which are equivalent to those of the Maxwell theory in curved spacetime, but with the usual metric $g_{\mu \nu}$ replaced by a unit-determinant metric $h_{\mu…
We analyze a beta function with the analytic form of Novikov-Shifman-Vainshtein-Zakharov result in the five dimensional gravity-dilaton environment. We show how dilaton inherits poles and fixed points of such beta function through the zeros…
The prepotential $F(a_i)$, defining the low-energy effective action of the $SU(N)$ ${\cal N}=2$ SUSY Yang-Mills theories, satisfies an enlarged set of the WDVV-like equations $F_iF_k^{-1}F_j = F_jF_k^{-1}F_i$ for any triple $i,j,k =…
This is a sequel of our paper hep-th/0606125 in which we have studied the {\cal N}=1 SU(N) SYM theory obtained as a marginal deformation of the {\cal N}=4 theory, with a complex deformation parameter \beta and in the planar limit. There we…
The $O(d,d)$ invariant worldsheet theory for bosonic string theory with $d$ abelian isometries is employed to compute the beta functions and Weyl anomaly at one-loop. We show that vanishing of the Weyl anomaly coefficients implies the…
We prove a duality, recently conjectured in arXiv:1103.5726, which relates the F-terms of supersymmetric gauge theories defined in two and four dimensions respectively. The proof proceeds by a saddle point analysis of the four-dimensional…
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…