Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2004-09-30
Phys.Lett. B610 (2005) 115-121
Physics
High Energy Physics
High Energy Physics - Theory
Minor changes, added one citation, version accepted for publication
Scientific paper
10.1016/j.physletb.2005.01.077
We demonstrate the irreversibility of a wide class of world-sheet renormalization group (RG) flows to first order in $\alpha'$ 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).
Oliynyk Todd
Suneeta V.
Woolgar Eric
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