Fluid Membranes and 2d Quantum Gravity

Abstract

We study the RG flow of two dimensional (fluid) membranes embedded in Euclidean D-dimensional space using functional RG methods based on the effective average action. By considering a truncation ansatz for the effective average action with both extrinsic and intrinsic curvature terms we derive a system of beta functions for the running surface tension, bending rigidity and Gaussian rigidity. We look for non-trivial fixed points but we find no evidence for a crumpling transition at $T\ne 0$. Finally, we propose to identify the $D\to 0$ limit of the theory with two dimensional quantum gravity. In this limit we derive new beta functions for both cosmological and Newton's constants.

16 pages, 1 figure

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Cited by in corpus (15)

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• RG flow equations for the proper-vertices of the background effective average action
• Scaling and Renormalization in two dimensional Quantum Gravity
• Symmetry breaking and lattice kirigami: finite temperature effects
• Renormalization of multicritical scalar models in curved space
• On quantum gravity, Asymptotic Safety, and paramagnetic dominance
• Renormalization Group Flow of Hexatic Membranes
• Auxiliary fields approach to shift-symmetric theories: the ${\phi }^4$ derivative theory and the crumpled-to-flat transition of membranes at two-loop order
• Effective models of membranes from symmetry breaking