A manifestly gauge invariant exact renormalization group

Abstract

In these lectures we describe the construction of a gauge invariant renormalization group equation for pure non-Abelian gauge theory. In the process, a non-perturbative gauge invariant continuum Wilsonian effective action is precisely defined. The formulation makes sense without gauge fixing and thus manifest gauge invariance may be preserved at all stages. In the large N limit (of SU(N) gauge theory) the effective action simplifies: it may be expressed through a path integral for a single particle whose trajectory describes a Wilson loop. Regularization is achieved with the help of a set of Pauli-Villars fields whose formulation follows naturally in this picture. Finally, we show how the one loop beta function was computed, for the first time without any gauge fixing.

Invited lectures at the Workshop on the Exact Renormalization Group, Faro, Portugal, Sept. 10-12, 1998. 32 pages including 24 figs. Conventions and notation changed to correspond to imminent papers, plus minor corrections

References in corpus (7)

• The Exact Renormalisation Group and Approximate Solutions
• On the Holographic Renormalization Group
• Elements of the Continuous Renormalization Group
• RG-Flow, Gravity and the Cosmological Constant
• On the construction of renormalized gauge theories using renormalization group techniques
• Exact Renormalization Group and Loop Equation
• New Developments in the Continuous Renormalization Group

Cited by in corpus (21)

• Holographic and Wilsonian Renormalization Groups
• Ghost D-branes
• On the UV structure of quantum unimodular gravity
• A Manifestly Gauge Invariant, Continuum Calculation of the SU(N) Yang-Mills two-loop beta function
• A Note On Relation Between Holographic RG Equation And Polchinski's RG Equation
• Exact scheme independence at one loop
• Manifestly diffeomorphism invariant classical Exact Renormalization Group
• Higgs inflation and quantum gravity: An exact renormalisation group approach
• BRS Symmetry, the Quantum Master Equation, and the Wilsonian Renormalization Group
• Triviality from the Exact Renormalization Group
• Gauge Consistent Wilson Renormalization Group I: Abelian Case
• Gauge Consistent Wilson Renormalization Group II: Non-Abelian Case
• Gauge Invariant Regularization in the AdS/CFT Correspondence and Ghost D-branes
• A Primer for Manifestly Gauge Invariant Computations in SU(N) Yang-Mills
• Exact renormalization group equation in presence of rescaling anomaly
• Equivalent Fixed-Points in the Effective Average Action Formalism
• Conformal anomaly from gauge fields without gauge fixing
• Gauge Invariant Cutoff QED
• Exact Renormalization Group and Loop Equation
• Quantum Field Theories with Symmetries in the Wilsonian Exact Renormalization Group
• Manifestly gauge invariant exact renormalization group for quantum electrodynamics