Background field method in the Wilson formulation

A cutoff regularization for a pure Yang-Mills theory is implemented within the background field method keeping explicit the gauge invariance of the effective action. The method has been applied to compute the beta function at one loop order.Comment: LaTex 13 pages, 1 figure; to appear in Nucl.Phys.

The Ward Identity from the Background Field Dependence of the Effective Action

The dependence of the effective action for gauge theories on the background field obeys an exact identity. We argue that for Abelian theories the Ward identity follows from the more general background field identity. This observation is particularly relevant for the anomalous Ward identity valid for gauge theories with an effective infrared cutoff as used for flow equations.Comment: 8 page

Spontaneous symmetry breaking with Wilson renormalization group

We study the conditions under which a symmetry is spontaneously broken in the Wilson renormalization group formulation. Both for a global and local symmetry, the result is that in perturbation theory one has to perform a fine tuning of the boundary conditions for the flow of the relevant couplings. We consider in detail the discrete $Z_2$ case and the Abelian Higgs model.Comment: 19 pages, latex, no figure

Beta function and infrared renormalons in the exact Wilson renormalization group in Yang-Mills theory

We discuss the relation between the Gell-Mann-Low beta function and the ``flowing couplings'' of the Wilsonian action S_\L[\phi] of the exact renormalization group (RG) at the scale \L. This relation involves the ultraviolet region of \L so that the condition of renormalizability is equivalent to the Callan-Symanzik equation. As an illustration, by using the exact RG formulation, we compute the beta function in Yang-Mills theory to one loop (and to two loops for the scalar case). We also study the infrared (IR) renormalons. This formulation is particularly suited for this study since: $i$) \L plays the r\^ole of a IR cutoff in Feynman diagrams and non-perturbative effects could be generated as soon as \L becomes small; $ii$) by a systematical resummation of higher order corrections the Wilsonian flowing couplings enter directly into the Feynman diagrams with a scale given by the internal loop momenta; $iii$) these couplings tend to the running coupling at high frequency, they differ at low frequency and remain finite all the way down to zero frequency.Comment: 19 pages, 6 figures, LaTex, uses epsfig, rotatin

Wilson Renormalization Group for Supersymmetric Gauge Theories and Gauge Anomalies

We extend the Wilson renormalization group (RG) to supersymmetric theories. As this regularization scheme preserves supersymmetry, we exploit the superspace technique. To set up the formalism we first derive the RG flow for the massless Wess-Zumino model and deduce its perturbative expansion. We then consider N=1 supersymmetric Yang-Mills and show that the local gauge symmetry -broken by the regularization- can be recovered by a suitable choice of the RG flow boundary conditions. We restrict our analysis to the first loop, the generalization to higher loops presenting no difficulty due to the iterative nature of the procedure. Furthermore, adding matter fields, we reproduce the one-loop supersymmetric chiral anomaly to the second order in the vector field.Comment: 22 pages, 1 Postscript figure, uses amssym

Gauge invariant action at the ultraviolet cutoff

We show that it is possible to formulate a gauge theory starting from a local action at the ultraviolet (UV) momentum cutoff which is BRS invariant. One has to require that fields in the UV action and the fields in the effective action are not the same but related by a local field transformation. The few relevant parameters involved in this transformation (six for the $SU(2)$ gauge theory), are perturbatively fixed by the gauge symmetry.Comment: 5 pages, Latex, no figure

New Macroeconomics and Credibility Analysis

This paper gives a general view of the new macroeconomics: the new Keynesian macroeconomics, the real business cycle models and the analysis of credibility of monetary policy. An outline of the chief technical features that distinguish the new Keynesian and the real business cycle formulations is provided, highlighting the specific characteristics that have been reconciled by the recent literature on credibility analysis. The point to be illustrated is that the combination of new Keynesian market failures and the new classical general equilibrium approach to macroeconomics leads to better microeconomic foundation for the credibility analyses of monetary policy that follow the Barro-Gordon notion of inflation bias of discretionary monetary policyNew Keynesian Macroeconomics, Credibility Analysis, Microeconomic Foundations

Exact supersymmetry on the lattice: the Wess-Zumino model

It is shown that the lattice Wess-Zumino model written in terms of Ginsparg-Wilson fermions is invariant under a generalized supersymmetry transformation which is determined by an iterative procedure in the coupling constant. This transformation is non-linear in the scalar fields and depends on the superpotential parameters. The implications of this lattice invariance are discussed.Comment: 3 pages, Lattice2004(theory), Fermilab, June 21-26, 200