Properties of a proposed background independent exact renormalization group
arXiv:2210.00492 · doi:10.1103/PhysRevD.107.065012
Abstract
We explore the properties of a recently proposed background independent exact renormalization group approach to gauge theories and gravity. In the process we also develop the machinery needed to study it rigorously. The proposal comes with some advantages. It preserves gauge invariance manifestly, avoids introducing unphysical fields, such as ghosts and Pauli-Villars fields, and does not require gauge-fixing. However, we show that in the simple case of SU(N) Yang-Mills it does not completely regularise the longitudinal part of vertex functions already at one loop, invalidating certain methods for extracting universal components. Moreover we demonstrate a kind of no-go theorem: within the proposed structure, whatever choice is made for covariantisation and cutoff profiles, the two-point vertex flow equation at one loop cannot be both transverse, as required by gauge invariance, and fully regularised.
arXiv comment51 pages, no figures. Minor corrections. Version published in PRD
References in corpus (27)
- General relativity as an effective field theory: The leading quantum corrections
- Nonperturbative Evolution Equation for Quantum Gravity
- Nonperturbative Quantum Gravity
- Quantum Gravity from Causal Dynamical Triangulations: A Review
- Fundamentals of the Exact Renormalization Group
- A gauge invariant exact renormalization group I
- Functional Integration Over Geometries
- Exact Scheme Independence
- Higher covariant derivative regularization revisited
- Consistency of the Regularization of Gauge Theories by High Covariant Derivatives
- A Generalised Manifestly Gauge Invariant Exact Renormalisation Group for SU(N) Yang-Mills
- A gauge invariant exact renormalization group II
- A Manifestly Gauge Invariant, Continuum Calculation of the SU(N) Yang-Mills two-loop beta function
- A proposal for a manifestly gauge invariant and universal calculus in Yang-Mills theory
- Exact scheme independence at two loops
- Gauge invariant regularisation via SU(N|N)
- Exact scheme independence at one loop
- Manifestly diffeomorphism invariant classical Exact Renormalization Group
- A Manifestly Gauge Invariant and Universal Calculus for SU(N) Yang-Mills
- Scheme Independence to all Loops
- Background independent exact renormalisation
- An exact RG formulation of quantum gauge theory
- Scheme independence as an inherent redundancy in quantum field theory
- General Computations Without Fixing the Gauge
- A Primer for Manifestly Gauge Invariant Computations in SU(N) Yang-Mills
- A gauge invariant regulator for the ERG
- Conformal anomaly from gauge fields without gauge fixing