Background independent exact renormalisation
arXiv:2004.11409 · doi:10.1140/epjc/s10052-020-08803-0
Abstract
A geometric formulation of Wilson's exact renormalisation group is presented based on a gauge invariant ultraviolet regularisation scheme without the introduction of a background field. This allows for a manifestly background independent approach to quantum gravity and gauge theories in the continuum. The regularisation is a geometric variant of Slavnov's scheme consisting of a modified action, which suppresses high momentum modes, supplemented by Pauli-Villars determinants in the path integral measure. An exact renormalisation group flow equation for the Wilsonian effective action is derived by requiring that the path integral is invariant under a change in the cutoff scale while preserving quasi-locality. The renormalisation group flow is defined directly on the space of gauge invariant actions without the need to fix the gauge. We show that the one-loop beta function in Yang-Mills and the one-loop divergencies of General Relativity can be calculated without fixing the gauge. As a first non-perturbative application we find the form of the Yang-Mills beta function within a simple truncation of the Wilsonian effective action.
arXiv comment34 pages, v2: One reference added, minor modifications and typos fixed
References in corpus (74)
- Exact evolution equation for the effective potential
- Non-Perturbative Renormalization Flow in Quantum Field Theory and Statistical Physics
- Nonperturbative Evolution Equation for Quantum Gravity
- The Exact Renormalisation Group and Approximate Solutions
- Aspects of the Functional Renormalisation Group
- Super-renormalizable Quantum Gravity
- Quantum Gravity from Causal Dynamical Triangulations: A Review
- Introduction to the functional RG and applications to gauge theories
- Flow Equations for N Point Functions and Bound States
- Fundamentals of the Exact Renormalization Group
- Ultraviolet properties of f(R)-Gravity
- Chiral symmetry breaking in continuum QCD
- Matter matters in asymptotically safe quantum gravity
- On the renormalization group flow of f(R)-gravity
- Landau gauge Yang-Mills correlation functions
- Non-perturbative quark, gluon and meson correlators of unquenched QCD
- On the relation of quark confinement and chiral symmetry breaking
- Taming perturbative divergences in asymptotically safe gravity
- Asymptotic safety of gravity-matter systems
- Local Quantum Gravity
- The Gravitational Two-Loop Counterterm is Asymptotically Safe
- Towards apparent convergence in asymptotically safe quantum gravity
- Search of scaling solutions in scalar-tensor gravity
- En route to Background Independence: Broken split-symmetry, and how to restore it with bi-metric average actions
- Generalized Parametrization Dependence in Quantum Gravity
- A flow equation for f(R) gravity and some of its exact solutions
- Resolving Spacetime Singularities within Asymptotic Safety
- Aspects of asymptotic safety for quantum gravity
- Form Factors in Asymptotic Safety: conceptual ideas and computational toolbox
- Non-minimal coupling in Higgs-Yukawa model with asymptotically safe gravity
- Curvature dependence of quantum gravity
- Renormalization Group Equation and scaling solutions for f(R) gravity in exponential parametrization
- A gauge invariant exact renormalization group I
- A proper fixed functional for four-dimensional Quantum Einstein Gravity
- Functional Integration Over Geometries
- Consistent closure of renormalization group flow equations in quantum gravity
- Renormalisation of Newton's constant
- The QCD Phase Boundary from Quark-Gluon Dynamics
- Baryon number fluctuations at finite temperature and density
- Exact Scheme Independence
- Renormalisation group flows for gauge theories in axial gauges
- Higher covariant derivative regularization revisited
- Correlation functions on a curved background
- Background independence in a background dependent renormalization group
- Field Parametrization Dependence in Asymptotically Safe Quantum Gravity
- Renormalization Group Equation for gravity on hyperbolic spaces
- Gauges and functional measures in quantum gravity I: Einstein theory
- Large curvature and background scale independence in single-metric approximations to asymptotic safety
- Background independent exact renormalization group for conformally reduced gravity
- The background scale Ward identity in quantum gravity
- A gauge invariant exact renormalization group II
- Gauges and functional measures in quantum gravity II: Higher derivative gravity
- Manifestly Gauge Invariant QCD
- A proposal for a manifestly gauge invariant and universal calculus in Yang-Mills theory
- Physical renormalization schemes and asymptotic safety in quantum gravity
- Gauge-invariant fields and flow equations for Yang-Mills theories
- Exact scheme independence at two loops
- Infinite order quantum-gravitational correlations
- Frame (In)equivalence in Quantum Field Theory and Cosmology
- Scaling Exponents for Lattice Quantum Gravity in Four Dimensions
- Exact scheme independence at one loop
- Asymptotic safety and the cosmological constant
- Manifestly diffeomorphism invariant classical Exact Renormalization Group
- Non-Compact Pure Gauge QED in 3D is Free
- Splitting Ward identity
- Manifestly gauge invariant QED
- Split Weyl transformations in quantum gravity
- Covariant and background independent functional RG flow for the effective average action
- An exact RG formulation of quantum gauge theory
- RG flow equations for the proper-vertices of the background effective average action
- General Computations Without Fixing the Gauge
- On the scaling of composite operators in Asymptotic Safety
- Universality From Very General Nonperturbative Flow Equations in QCD
- Conformal anomaly from gauge fields without gauge fixing
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- Essential Quantum Einstein Gravity
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- Exploring new corners of asymptotically safe unimodular quantum gravity
- Configuration space for quantum gravity in a locally regularized path integral
- Properties of a proposed background independent exact renormalization group
- Background Effective Action with Nonlinear Massive Gauge Fixing
- Physics-informed operator flows and observables