Manifestly Gauge Invariant QCD

Abstract

Building on recent work in SU(N) Yang-Mills theory, we construct a manifestly gauge invariant exact renormalization group for QCD. A gauge invariant cutoff is constructed by embedding the physical gauge theory in a spontaneously broken SU(N|N) gauge theory, regularized by covariant higher derivatives. Intriguingly, the construction is most efficient if the number of flavours is a multiple of the number of colours. The formalism is illustrated with a very compact calculation of the one-loop beta function, achieving a manifestly universal result and without fixing the gauge.

30 pages, 6 figures

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Cited by in corpus (36)

• The nonperturbative functional renormalization group and its applications
• Investigating the Ultraviolet Properties of Gravity with a Wilsonian Renormalization Group Equation
• Derivation of the exact NSVZ beta-function in N=1 SQED, regularized by higher derivatives, by direct summation of Feynman diagrams
• Perturbation theory and non-perturbative renormalization flow in scalar field theory at finite temperature
• Calculation of two-loop beta-function for general N=1 supersymmetric Yang--Mills theory with the higher covariant derivative regularization
• Gauge-invariant fields and flow equations for Yang-Mills theories
• Manifestly diffeomorphism invariant classical Exact Renormalization Group
• Some non-renormalization theorems in Curci-Ferrari model
• Impact of generalized Yukawa interactions on the lower Higgs mass bound
• Gauge Invariant Summation of All QCD Virtual Gluon Exchanges
• Renormalization Group Flow as Optimal Transport
• BRST in the Exact RG
• Triviality from the Exact Renormalization Group
• On the construction of QED using ERG
• Background independent exact renormalisation
• Bayesian Renormalization
• BRST invariant RG flows
• Universality From Very General Nonperturbative Flow Equations in QCD
• Massless fermions in multi-flavor QED_2
• Wilsonian Renormalization of Noncommutative Scalar Field Theory
• Fixed point merger in the SU(N) gauge beta functions
• A Resummable beta-Function for Massless QED
• Construction of a Wilson action for the Wess-Zumino model
• Gradient flow exact renormalization group -- inclusion of fermion fields
• Gauge and Poincare' Invariant Regularization and Hopf Symmetries
• The analytic structure of the Landau gauge quark propagator from Padé analysis
• Conformal anomaly from gauge fields without gauge fixing
• Renormalization of QCD_2
• Gauge invariant composite operators of QED in the exact renormalization group formalism
• Factorization of integrals, defining the beta-function, into integrals of total derivatives in N=1 SQED, regularized by higher derivatives
• Gauge Invariant Exact Renormalization Group and Perfect Actions in the Open Bosonic String Theory
• An Extension of Pohlmeyer's Theorem
• Renormalizability of the dimension two gluon operator $A^2$ in a class of nonlinear covariant gauges
• Background Effective Action with Nonlinear Massive Gauge Fixing
• Sensitivity of Nonrenormalizable Trajectories to the Bare Scale
• Ground-state wave-functional in (2+1)-dimensional Yang-Mills theory: Abelian limit, spectrum and robustness