Beta function and asymptotic safety in three-dimensional higher derivative gravity

• Published in: Classical and quantum gravity Vol. 29; no. 20; pp. 205012 - 15
• Main Author: Ohta, Nobuyoshi
• Format: Journal Article
• Language: English
• Published: Bristol IOP Publishing 21.10.2012; Institute of Physics
• Subjects: Approximation; Asymptotic properties; asymptotic safety; beta function; Cosmological constant; Derivatives; Exact sciences and technology; General relativity and gravitation; Gravitation; higher derivative; Mathematical analysis; Physics; Quantum gravity; renormalization group; Three dimensional; Beta function; Cosmological constant; Cosmology; Gravitational constant; Curvature; Gravity
• ISSN: 0264-9381; 1361-6382
• DOI: 10.1088/0264-9381/29/20/205012

We study the quantum properties of the three-dimensional higher derivative gravity. In particular, we calculate the running of the gravitational and cosmological constants. The flow of these couplings shows that there exist both Gaussian and non-trivial fixed points in the theory, thus confirming that the theory is asymptotically safe. It is shown that the new massive gravity or f(R) gravity in three dimensions does not correspond to the fixed point within the approximation that the coefficients of the higher curvature terms are not subject to the flow. The fixed point value of the cosmological constant is found to be gauge-independent, positive and small. We also find that if we start with Einstein term with negative sign, the fixed point only exists when the coefficient of the Einstein term has positive sign.