Exact Symmetries realized on the Renormalized Group Flow

We show that symmetries are preserved exactly along the (Wilsonian) renormalization group flow, though the IR cutoff deforms concrete forms of the transformations. For a gauge theory the cutoff dependent Ward-Takahashi identity is written as the master equation in the antifield formalism: one may read off the renormalized BRS transformation from the master equation. The Maxwell theory is studied explicitly to see how it works. The renormalized BRS transformation becomes non-local but keeps off-shell nilpotency. Our formalism is applicable for a generic global symmetry. The master equation considered for the chiral symmetry provides us with the continuum analog of the Ginsparg-Wilson relation and the L{\" u}scher's symmetry.Comment: Latex, 10 page

Gauge-Invariant Renormalization Group at Finite Temperature

We propose a gauge-invariant version of Wilson Renormalization Group for thermal field theories in real time. The application to the computation of the thermal masses of the gauge bosons in an SU(N) Yang-Mills theory is discussed.Comment: 23 pages, latex2e, 1 EPS figure. The discussions of BRS identities and of the RG kernel have been modified. Final version, to appear on Nucl. Phys.

Exact Renormalization Group in Algebraic Noncovariant Gauges

I study a class of Wilsonian formulations of non-Abelian gauge theories in algebraic noncovariant gauges where the Wilsonian infrared cutoff $\Lambda$ is inserted as a mass term for the propagating fields. In this way the Ward-Takahashi identities are preserved to all scales. Nevertheless the BRS-invariance in broken and the theory is gauge-dependent and unphysical at $\Lambda\neq0$. Then I discuss the infrared limit $\Lambda\to0$. I show that the singularities of the axial gauge choice are avoided in planar gauge and in light-cone gauge. Finally the rectangular Wilson loop of size $2L\times 2T$ is evaluated at lowest order in perturbation theory and a noncommutativity between the limits $\Lambda\to0$ and $T\to\infty$ is pointed out.Comment: 6 pages, latex2e, Proceeding of the Second Conference on the Exact R

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.

Critical Behavior of phi^4-Theory from the Thermal Renormalization Group

We discuss the universal critical behavior of a selfinteracting scalar field theory at finite temperature as obtained from approximate solutions to nonperturbative renormalization group (RG) equations. We employ a formulation of the RG-equations in real-time formalism which is particularly well suited for a discussion of the thermal behavior of theories which are weakly coupled at T=0. We obtain the equation of state and critical exponents of the theory with a few percent accuracy even for a relatively simple approximation to the exact renormalization group equations.Comment: Revised version, to appear in Phys. Lett. B; References and discussion adde

Axial anomalies in gauge theory by exact renormalization group method

The global chiral symmetry of a $SU(2)$ gauge theory is studied in the framework of renormalization group (RG). The theory is defined by the RG flow equations in the infrared cutoff \L and the boundary conditions for the relevant couplings. The physical theory is obtained at \L=0. In our approach the symmetry is implemented by choosing the boundary conditions for the relevant couplings not at the ultraviolet point \L=\L_0\to\infty but at the physical value \L=0. As an illustration, we compute the triangle axial anomalies.Comment: 11 pages + 1 appended EPS figure, LaTeX, UPRF 94-39