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Redundant operators in the exact renormalisation group and in the f(R) approximation to asymptotic safety

Redundant operators in the exact renormalisation group and in the f(R) approximation to asymptotic safety
Redundant operators in the exact renormalisation group and in the f(R) approximation to asymptotic safety
In this paper we review the definition and properties of redundant operators in the exact renormalisation group. We explain why it is important to require them to be eigenoperators and why generically they appear only as a consequence of symmetries of the particular choice of renormalisation group equations. This clarifies when Newton’s constant and or the cosmological constant can be considered inessential. We then apply these ideas to the Local Potential Approximation and approximations of a similar spirit such as the f (R) approximation in the asymptotic safety programme in quantum gravity. We show that these approximations can break down if the fixed point does not support a ‘vacuum’ solution in the appropriate domain: all eigenoperators become redundant and the physical space of perturbations collapses to a point. We show that this is the case for the recently discovered lines of fixed points in the f (R) flow equations.
models of quantum gravity, nonperturbative effects, renormalization group
1-25
Dietz, Juergen A.
25b4e470-3534-476d-8844-ada94b16feeb
Morris, Tim R.
a9927d31-7a12-4188-bc35-1c9d3a03a6a6
Dietz, Juergen A.
25b4e470-3534-476d-8844-ada94b16feeb
Morris, Tim R.
a9927d31-7a12-4188-bc35-1c9d3a03a6a6

Dietz, Juergen A. and Morris, Tim R. (2013) Redundant operators in the exact renormalisation group and in the f(R) approximation to asymptotic safety. Journal of High Energy Physics, 2013 (64), 1-25. (doi:10.1007/JHEP07(2013)064).

Record type: Article

Abstract

In this paper we review the definition and properties of redundant operators in the exact renormalisation group. We explain why it is important to require them to be eigenoperators and why generically they appear only as a consequence of symmetries of the particular choice of renormalisation group equations. This clarifies when Newton’s constant and or the cosmological constant can be considered inessential. We then apply these ideas to the Local Potential Approximation and approximations of a similar spirit such as the f (R) approximation in the asymptotic safety programme in quantum gravity. We show that these approximations can break down if the fixed point does not support a ‘vacuum’ solution in the appropriate domain: all eigenoperators become redundant and the physical space of perturbations collapses to a point. We show that this is the case for the recently discovered lines of fixed points in the f (R) flow equations.

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Published date: July 2013
Keywords: models of quantum gravity, nonperturbative effects, renormalization group
Organisations: Physics & Astronomy

Identifiers

Local EPrints ID: 368136
URI: http://eprints.soton.ac.uk/id/eprint/368136
PURE UUID: 177ba5cd-92d5-4afc-b81d-a533e764ddb5
ORCID for Tim R. Morris: ORCID iD orcid.org/0000-0001-6256-9962

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Date deposited: 18 Aug 2014 14:44
Last modified: 07 Oct 2020 02:56

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