(Non) Gauge Invariance of Wilsonian Effective Actions in (Supersymmetric) Gauge Theories : A Critical Discussion
arXiv:0705.0362 · doi:10.1016/j.aop.2008.01.002
Abstract
We give a detailed critical discussion of the properties of Wilsonian effective actions, defined by integrating out all modes above a given scale . In particular, we provide a precise and relatively convenient prescription how to implement the infrared cutoff in any loop integral that is manifestly Lorentz invariant and also preserves global linear symmetries such as e.g. supersymmetry. We discuss the issue of gauge invariance of effective actions in general and in particular when using background field gauge. Our prescription for the IR cutoff (as any such prescription) breaks the gauge symmetry. Using our prescription, we have explicitly computed, at one loop, many terms of the Wilsonian effective action for general gauge theories, involving bosonic and fermionic matter fields of arbitrary masses and in arbitrary representations, exhibiting the non-gauge invariant (as well as the gauge invariant) terms. However, for supersymmetric gauge theories all non-gauge invariant terms cancel within each supermultiplet. This is strong evidence that in supersymmetric gauge theories this indeed defines a Lorentz, susy and gauge invariant Wilsonian effective action. As a byproduct, we obtain the explicit one-loop Wilsonian couplings for all higher-derivative terms in the effective action of arbitrary supersymmetric gauge theories.
arXiv comment39 pages, 3 figures; several comments in sect. 2.6 and references are added
References in corpus (18)
- Non-Perturbative Renormalization Flow in Quantum Field Theory and Statistical Physics
- Aspects of the Functional Renormalisation Group
- Naturalness Versus Supersymmetric Non-renormalization Theorems
- Introduction to Effective Field Theory
- Abelian chiral gauge theories on the lattice with exact gauge invariance
- Field Dependent Gauge Couplings in Locally Supersymmetric Effective Quantum Field Theories
- Flow Equations and BRS Invariance for Yang-Mills Theories
- The Background Field Method for N = 2 Super Yang-Mills Theories in Harmonic Superspace
- Gauge invariance and background field formalism in the exact renormalisation group
- Supersymmetric non-abelian Born-Infeld revisited
- Ward identities and Wilson renormalization group for QED
- Non-perturbative thermal flows and resummations
- Higher-Derivative Corrections to the Non-Abelian Born-Infeld Action
- A Generalised Manifestly Gauge Invariant Exact Renormalisation Group for SU(N) Yang-Mills
- Wilson Renormalization Group for Supersymmetric Gauge Theories and Gauge Anomalies
- On the construction of QED using ERG
- Effective Average Action in N=1 Super-Yang-Mills Theory
- Invariant Regularization of Supersymmetric Chiral Gauge Theory