The Generalized Ricci Flow for 3D Manifolds with One Killing Vector

Details The Generalized Ricci Flow for 3D Manifolds with One Killing Vector The Generalized Ricci Flow for 3D Manifolds with One Killing Vector

2005-09-13

arxiv.org/abs/hep-th/0509091v1

J.Math.Phys. 47 (2006) 032304

Physics

High Energy Physics

High Energy Physics - Theory

Scientific paper

We consider 3D flow equations inspired by the renormalization group (RG) equations of string theory with a three dimensional target space. By modifying the flow equations to include a U(1) gauge field, and adding carefully chosen De Turck terms, we are able to extend recent 2D results of Bakas to the case of a 3D Riemannian metric with one Killing vector. In particular, we show that the RG flow with De Turck terms can be reduced to two equations: the continual Toda flow solved by Bakas, plus its linearizaton. We find exact solutions which flow to homogeneous but not always isotropic geometries.

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