相关论文: Swampland, Gradient Flow and Infinite Distance
In this paper we study $n$-dimensional Ricci flows $(M^n,g(t))_{t\in [0,T)},$ where $T< \infty$ is a potentially singular time, and for which the spatial $L^p$ norm, $p>\frac n 2$, of the scalar curvature is uniformly bounded on $[0,T).$ In…
We develop different synthetic notions of Ricci flow in the setting of time-dependent metric measure spaces based on ideas from optimal transport. They are formulated in terms of dynamic convexity and local concavity of the entropy along…
We develop a compactness theory for super Ricci flows, which lays the foundations for the partial regularity theory in [Bam20b]. Our results imply that any sequence of super Ricci flows of the same dimension that is pointed in an…
In this note, we propose a generalized notion of distance between vacua in the theory of a scalar field $\phi$ with scalar potential $V(\phi)$ coupled to gravity. We propose the normalized tension of domain wall connecting different field…
The Ryu-Takayanagi conjecture establishes a remarkable connection between quantum systems and geometry. Specifically, it relates the entanglement entropy to minimal surfaces within the setting of AdS/CFT correspondence. This Letter shows…
Generalized global symmetries are a common feature of many quantum field theories decoupled from gravity. By contrast, in quantum gravity / the Swampland program, it is widely expected that all global symmetries are either gauged or broken,…
We show that a complete Ricci flow of bounded curvature which begins from a manifold with a Ricci lower bound, local entropy bound, and small local scale-invariant integral curvature control will have global point-wise curvature control at…
We show that the configuration space over a manifold M inherits many curvature properties of the manifold. For instance, we show that a lower Ricci curvature bound on M implies for the configuration space a lower Ricci curvature bound in…
In this paper we study the evolution of almost non-negatively curved (possibly singular) three dimensional metric spaces by Ricci flow. The non-negatively curved metric spaces which we consider arise as limits of smooth Riemannian manifolds…
We study noncommutative Ricci flow in a finite dimensional representation of a noncommutative torus. It is shown that the flow exists and converges to the flat metric. We also consider the evolution of entropy and a definition of scalar…
Geometrical tools, used in Einstein's general relativity (GR), are applied to dynamo theory, in order to obtain fast dynamo action bounds to magnetic energy, from Killing symmetries in Ricci flows. Magnetic field is shown to be the shear…
The Swampland Distance Conjecture (SDC) states that, as we move towards an infinite distance point in moduli space, a tower of states becomes exponentially light with the geodesic distance in any consistent theory of Quantum Gravity.…
We show the existence of a solution to the Ricci flow with a compact length space of bounded curvature, i.e., a space that has curvature bounded above and below in the sense of Alexandrov, as its initial condition. We show that this flow…
We review and extend the recently proposed model of combinatorial quantum gravity. Contrary to previous discrete approaches, this model is defined on (regular) random graphs and is driven by a purely combinatorial version of Ricci…
We study a new notion of Ricci curvature that applies to Markov chains on discrete spaces. This notion relies on geodesic convexity of the entropy and is analogous to the one introduced by Lott, Sturm, and Villani for geodesic measure…
In any consistent effective field theory of quantum gravity limits of infinite field distance are expected to lead to the EFT breakdown due to the appearance of an infinite tower of light states, as predicted by the Distance Conjecture. We…
We investigate a new geometric flow which consists of a coupled system of the Ricci flow on a closed manifold M with the harmonic map flow of a map phi from M to some closed target manifold N with a (possibly time-dependent) positive…
We study a class of fourth order curvature flows on a compact Riemannian manifold, which includes the gradient flows of a number of quadratic geometric functionals, as for instance the L2 norm of the curvature. Such flows can develop a…
The RG-2 flow is the two-loop approximation for the world-sheet non-linear sigma model renormalization group flow. The first truncation of the flow is the well known Ricci flow, at two loops higher order curvature terms appear, changing…
Recent developments in string theory suggest that string theory landscape of vacua is vast. It is natural to ask if this landscape is as vast as allowed by consistent-looking effective field theories. We use universality ideas from string…