https://neckpinch.com/authors/dieter-lust/New arXiv papers by Dieter Lust, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2412.10364arxiv:2412.10364Fri, 13 Dec 2024 00:00:00 GMTSaskia Demulder, Dieter Lust, Thomas Raml — The Swampland Distance Conjecture postulates the emergence of an infinite tower of massless states when approaching infinite-distance points in moduli space. However, most string backgrounds are supported by fluxes, and therefore depart from the purely geometric paradigm. This fact requires an extension of the Swampland conjectures to scalar field spaces with non-trivial potentials, rather than just moduli spaces. To address this task, we utilise geometric flows, in particular generalised Ricci flow, to probe the associated scalar field spaces. Considering internal spaces supported by three-form fluxes, we first show that the distance defined in terms of the Perelman entropy functional needs to be refined in order to encompass fluxes. Doing so, we extend the Ricci Flow Conjecture to include Kalb-Ramond flux besides the metric and the dilaton field. This allows us to probe infinite-distance points within these scalar field spaces in a purely geometric way. We subsequently construct a geometric flow for internal manifolds supported by Ramond-Ramond fluxes and discuss its role in the Ricci Flow Conjecture. Our analysis suggests that in the presence of fluxes the Distance Conjecture might be better characterised in terms of a cost function on the space of metrics, rather than a genuine distance.Ricci flowGeneralized & G₂ flowsPerelman entropySmale conjecture & diffeomorphismsPhysics https://arxiv.org/abs/2210.14705arxiv:2210.14705Wed, 26 Oct 2022 00:00:00 GMTDavide De Biasio, Julian Freigang, Dieter Lust, Toby Wiseman — Ricci flow is a natural gradient flow of the Einstein-Hilbert action. Here we consider the analog for the Einstein-Maxwell action, which gives Ricci flow with a stress tensor contribution coupled to a Yang-Mills flow for the Maxwell field. We argue that this flow is well-posed for static spacetimes with pure electric or magnetic potentialsand show it preserves both non-extremal and extremal black hole horizons. In the latter case we find the flow of the near horizon geometry decouples from that of the exterior. The Schwarzschild black hole is an unstable fixed point of Ricci flow for static spacetimes. Here we consider flows of the Reissner-Nordström (RN) fixed point. The magnetic RN solution becomes a stable fixed point of the flow for sufficient charge. However we find that the electric RN black hole is always unstable. Numerically solving the flow starting with a spherically symmetric perturbation of a non-extremal RN solution, we find similar behaviour in the electric case to the Ricci flows of perturbed Schwarzschild, namely the horizon shrinks to a singularity in finite time or expands forever. In the magnetic case, a perturbed unstable RN solution has a similar expanding behaviour, but a perturbation that decreases the horizon size flows to a stable black hole solution rather than a singularity. For extremal RN we solve the near horizon flow for spherical symmetry exactly, and see in the electric case two unstable directions which flow to singularities in finite flow time. However, even turning these off, and fixing the near horizon geometry to be that of RN, we numerically show that the flows appear to become singular in the vicinity of its horizon.Ricci flowSingularitiesStability & uniquenessRotational symmetry & warped productsPhysicsNumerics & visualization https://arxiv.org/abs/2209.10297arxiv:2209.10297Wed, 21 Sep 2022 00:00:00 GMTDavid Martín Velázquez, Davide De Biasio, Dieter Lust — In the following work, an attempt to conciliate the Ricci flow conjecture and the Cobordism conjecture, stated as refinements of the Swampland distance conjecture and of the No global symmetries conjecture respectively, is presented. This is done by starting from a suitable manifold with trivial cobordism class, applying surgery techniques to Ricci flow singularities and trivialising the cobordism class of one of the resulting connected components via the introduction of appropriate defects. The specific example of Ω^(SO)₄ is studied in detail. A connection between the process of blowing up a point of a manifold and that of taking the connected sum of such with ℂP}ⁿ is explored. Hence, the problem of studying the Ricci flow of a K3 whose cobordism class is trivialised by the addition of 16 copies of ℂP}² is tackled by applying both the techniques developed in the previous sections and the classification of singularities in terms of ADE groups.Ricci flowSingularitiesSurgery