Effective metric Lagrangians from an underlying theory with two propagating degrees of freedom

Journal Article · Thu Apr 15 04:00:00 EDT 2010 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.81.084026· OSTI ID:21409605

Krasnov, Kirill ^[1]

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1. School of Mathematical Sciences, University of Nottingham, Nottingham, NG7 2RD (United Kingdom)

We describe an infinite-parametric class of effective metric Lagrangians that arise from an underlying theory with two propagating degrees of freedom. The Lagrangians start with the Einstein-Hilbert term, continue with the standard R{sup 2}, (Ricci){sup 2} terms, and in the next order contain (Riemann){sup 3} as well as on-shell vanishing terms. This is exactly the structure of the effective metric Lagrangian that renormalizes quantum gravity divergences at two loops. This shows that the theory underlying the effective field theory of gravity may have no more degrees of freedom than is already contained in general relativity. We show that the reason why an effective metric theory may describe just two propagating degrees of freedom is that there exists a (nonlocal) field redefinition that maps an infinitely complicated effective metric Lagrangian to the usual Einstein-Hilbert one. We describe this map for our class of theories and, in particular, exhibit it explicitly for the (Riemann){sup 3} term.

• OSTI ID: 21409605
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 8 Vol. 81; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BANACH SPACE
DEGREES OF FREEDOM
FIELD THEORIES
FUNCTIONS
GENERAL RELATIVITY THEORY
GRAVITATION
HILBERT SPACE
LAGRANGIAN FUNCTION
MATHEMATICAL SPACE
METRICS
QUANTUM FIELD THEORY
QUANTUM GRAVITY
RELATIVITY THEORY
RENORMALIZATION
SPACE