Short-time existence for the second order renormalization group flow in general dimensions

Abstract

We prove local existence for the second order Renormalization Group flow initial value problem on closed Riemannian manifolds $(M,g)$ in general dimensions, for initial metrics whose sectional curvatures $K_P$ satisfy the condition $1+\alpha K_P > 0$, at all points $p \in M$ and planes $P \subset T_p M$. This extends results previously proven for two and three dimensions.