Properties of a proposed background independent exact renormalization group
Properties of a proposed background independent exact renormalization group
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 fails to properly regularise all vertex functions already at one loop, and thus that the flow equation is not divergence-free. 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 properly regularised.
hep-th, gr-qc
Mandric, Vlad-Mihai
04dbbef5-4c78-4ab4-8e0f-ed2c86554c14
Morris, Tim R.
a9927d31-7a12-4188-bc35-1c9d3a03a6a6
17 March 2023
Mandric, Vlad-Mihai
04dbbef5-4c78-4ab4-8e0f-ed2c86554c14
Morris, Tim R.
a9927d31-7a12-4188-bc35-1c9d3a03a6a6
Mandric, Vlad-Mihai and Morris, Tim R.
(2023)
Properties of a proposed background independent exact renormalization group.
Physical Review D, 107, [065012].
(doi:10.48550/arXiv.2210.00492).
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 fails to properly regularise all vertex functions already at one loop, and thus that the flow equation is not divergence-free. 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 properly regularised.
Text
2210.00492v1
- Author's Original
Restricted to Repository staff only
Request a copy
Text
PhysRevD.107.065012
- Version of Record
More information
Submitted date: 4 October 2022
Accepted/In Press date: 1 March 2023
Published date: 17 March 2023
Additional Information:
51 pages, no figures
Keywords:
hep-th, gr-qc
Identifiers
Local EPrints ID: 472286
URI: http://eprints.soton.ac.uk/id/eprint/472286
ISSN: 2470-0010
PURE UUID: f148f675-cbad-4efc-9f20-d9ea52d36355
Catalogue record
Date deposited: 30 Nov 2022 17:46
Last modified: 18 Mar 2024 02:32
Export record
Altmetrics
Download statistics
Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.
View more statistics
