2004/10/31 by Todd A. Oliynyk, T Oliynyk, Vardarajan Suneeta +3
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Curvature #Entropy (arrow of time) #Flow (mathematics) #Geometric Analysis and Curvature Flows #Geometry #Mathematical analysis #Mathematical physics #Mathematics #Monotonic function #Physics #Pure mathematics #Quantum mechanics #Renormalization group #Ricci curvature #Ricci flow #Scalar (mathematics) #Scalar curvature #gr-qc #hep-th #math-ph #math.DG #math.MP
paper · pdf · doi:10.1016/j.physletb.2005.01.077
published as Phys.Lett. B610 (2005) 115-121 · Minor changes, added one citation, version accepted for publication
arxiv created 2005/02/01 · openalex publication_date 2005/02/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We demonstrate the irreversibility of a wide class of world-sheet renormalization group (RG) flows to first order in α′ in string theory. Our techniques draw on the mathematics of Ricci flows, adapted to asymptotically flat target manifolds. In the case of somewhere-negative scalar curvature (of the target space), we give a proof by constructing an entropy that increases monotonically along the flow, based on Perelman's Ricci flow entropy. One consequence is the absence of periodic solutions, and we are able to give a second, direct proof of this. If the scalar curvature is everywhere positive, we instead construct a regularized volume to provide an entropy for the flow. Our results are, in a sense, the analogue of Zamolodchikov's c-theorem for world-sheet RG flows on noncompact spacetimes (though our entropy is not the Zamolodchikov C-function).