2013/06/05 by Juergen A. Dietz, Tim R. Morris, Dietz, Juergen A. +1 · 3 citations
Physics and Astronomy · #Cosmology and Gravitation Theories #Black Holes and Theoretical Physics #Noncommutative and Quantum Gravity Theories
paper · pdf · doi:10.48550/arxiv.1306.1223
In this paper we review the definition and properties of redundant operators\nin the exact renormalisation group. We explain why it is important to require\nthem to be eigenoperators and why generically they appear only as a consequence\nof symmetries of the particular choice of renormalisation group equations. This\nclarifies when Newton's constant and or the cosmological constant can be\nconsidered inessential. We then apply these ideas to the Local Potential\nApproximation and approximations of a similar spirit such as the f(R)\napproximation in the asymptotic safety programme in quantum gravity. We show\nthat these approximations can break down if the fixed point does not support a\n`vacuum' solution in the appropriate domain: all eigenoperators become\nredundant and the physical space of perturbations collapses to a point. We show\nthat this is the case for the recently discovered lines of fixed points in the\nf(R) flow equations.\n