The Cauchy problem for gradient generalized Ricci solitons on a bundle gerbe
Severin Bunk, Miguel Pino, C. S. Shahbazi
TL;DR
This work establishes well-posedness for the analytic Cauchy problem of gradient generalized Ricci solitons on abelian bundle gerbes by moving to the Einstein frame, performing a time-dependent reduction to a Cauchy surface, and applying the Cauchy–Kovalevskaya theorem to analytic initial data. It introduces and analyzes the automorphism 2-group of bundle gerbes, and shows how self-similar flows are generated by families of higher automorphisms, leading to a precise SOLITON characterization. A detailed reduction on reducible bundle gerbes yields evolution equations and time-dependent constraints that govern the Cauchy problem, with a proof of short-time existence under analytic data. In three dimensions, the authors solve the constraint system on any conformal class of a punctured surface and deduce the existence of infinitely many NS gradient generalized Ricci solitons embedded in 3-manifolds, highlighting a rich landscape of solitons and topologies. The results bridge higher geometry with NS-NS supergravity and pave the way for extending such analyses to heterotic solitons and broader geometric contexts.
Abstract
We prove well-posedness of the analytic Cauchy problem for gradient generalized Ricci solitons on an abelian bundle gerbe and solve the initial data equations on every compact Riemann surface. Along the way, we provide a novel characterization of the self-similar solutions of the generalized Ricci flow by means of families of automorphisms of the underlying abelian bundle gerbe covering families of diffeomorphisms isotopic to the identity.