We propose a novel scheme for the exact renormalisation group motivated by the desire of reducing the complexity of practical computations. The key idea is to specify renormalisation conditions for all inessential couplings, leaving us with the task of computing only the flow of the essential ones. To achieve this aim, we utilise a renormalisation group equation for the effective average action which incorporates general non-linear field reparameterisations. A prominent feature of the scheme is that, apart from the renormalisation of the mass, the propagator evaluated at any constant value of the field maintains its unrenormalised form. Conceptually, the simplifications can be understood as providing a description based only on quantities that enter expressions for physical observables since the redundant, non-physical content is automatically disregarded. To exemplify the scheme's utility, we investigate the Wilson-Fisher fixed point in three dimensions at order two in the derivative expansion. In this case, the scheme removes all order $\partial^2$ operators apart from the canonical term. Further simplifications occur at higher orders in the derivative expansion. Although we concentrate on a minimal scheme that reduces the complexity of computations, we propose more general schemes where inessential couplings can be tuned to optimise a given approximation. We further discuss the applicability of the scheme to a broad range of physical theories.
Cited by 4
Braun et al., Renormalised spectral flows
SciPost Phys. Core 6, 061 (2023) [Crossref]
Ihssen et al., Functional flows for complex effective actions
SciPost Phys. 15, 074 (2023) [Crossref]
Gies et al., Asymptotically safe Hilbert–Palatini gravity in an on-shell reduction scheme
Eur. Phys. J. C 83, 173 (2023) [Crossref]
Gao et al., Determining wave equations in holographic QCD from Wilsonian renormalization group
Phys. Rev. D 106, 126003 (2022) [Crossref]
Authors / Affiliations: mappings to Contributors and OrganizationsSee all Organizations.
- 1 Scuola Internazionale Superiore di Studi Avanzati / International School for Advanced Studies [SISSA]
- 2 Istituto Nazionale di Fisica Nucleare (presso la SISSA) / National Institute of Nuclear Physics (at SISSA) [INFN at SISSA]
- 3 Sorbonne Université / Sorbonne University