We show that for two-dimensional manifolds M with negative Euler characteristics, there exist subsets of the space of smooth Riemannian metrics which are invariant and either parabolic or backwards-parabolic for the second-order RG flow. We also show that solutions exist globally on these sets. Finally, we establish the existence of an eternal solution that has both a UV and IR limit, and passes through regions where the flow is parabolic and backwards-parabolic.
|Pages (from-to)||105020 - 105027|
|Number of pages||8|
|Journal||Letters in Mathematical Physics|
|Publication status||Published - 2009|