相关论文: Swampland, Gradient Flow and Infinite Distance

The Swampland Distance Conjecture (SDC) states that, for any infinite-distance limit in the moduli space of a quantum gravity effective field theory (EFT), there should exist an infinite tower of states that become exponentially light.…

We prove the existence of Ricci flow starting from a class of metrics with unbounded curvature, which are doubly-warped products over an interval with a spherical factor pinched off at an end. These provide a forward evolution from some…

The swampland conjectures seek to distinguish effective field theories which can be consistently embedded in a theory of quantum gravity from those which can not (and are hence referred to as being in the swampland). We consider two such…

We consider the swampland distance and de Sitter conjectures, of respective order one parameters $\lambda$ and $c$. Inspired by the recent Trans-Planckian Censorship conjecture (TCC), we propose a generalization of the distance conjecture,…

Swampland criteria like the Weak Gravity Conjecture should not only apply to particles, but also to other lower-codimension charged objects in 4d EFTs like strings and membranes. However, the description of the latter is in general subtle…

The Distance Conjecture holds that any infinite-distance limit in the scalar field moduli space of a consistent theory of quantum gravity must be accompanied by a tower of light particles whose masses scale exponentially with proper field…

A framework of quantum spacetime reference frame is proposed and reviewed, in which the quantum spacetime at the Gaussian approximation is deformed by the Ricci flow. At sufficient large scale, the Ricci flow not only smooths out local…

We establish a short-time existence theory for complete Ricci flows under scaling-invariant curvature bounds, starting from rotationally symmetric metrics on $\mathbb{R}^{n+1}$ that are noncollapsed at infinity, without assuming bounded…

We perform a systematic study of the applicability of swampland constraints to theories of localized gravity. We find that these gravity theories can violate swampland constraints, but can be reconciled with them when coupled to a…

We conjecture and present evidence that any effective field theory coupled to gravity in flat space admits at most a finite number of fine tunings, depending on the amount of supersymmetry and spacetime dimension. In particular, this means…

The ``Swampland Program'' aims to discriminate consistent-looking effective field theories that do not admit a UV completion in quantum gravity from those that do. While most often developed under the umbrella of string theory, several…

In Riemannian geometry, the Ricci flow is the analogue of heat diffusion; a deformation of the metric tensor driven by its Ricci curvature. As a step towards resolving the problem of time in quantum gravity, we attempt to merge the Ricci…

This paper establishes a unified framework integrating geometric flows with deep learning through three fundamental innovations. First, we propose a thermodynamically coupled Ricci flow that dynamically adapts parameter space geometry to…

Distances in the conformal manifold, the space of CFTs related by marginal deformations, can be measured in terms of the Zamolodchikov metric. Part of the CFT Distance Conjecture posits that points in this manifold where part of the…

We consider spacetime-dependent solutions to string theory models with tadpoles for dynamical fields, arising from non-trivial scalar potentials. The solutions have necessarily finite extent in spacetime, and are capped off by boundaries at…

In this paper, we define a reduced distance function based at a point at the singular time $T<\infty$ of a Ricci flow. We also show the monotonicity of the corresponding reduced volume based at time T, with equality iff the Ricci flow is a…

In this paper we give an explicit bound of $\Delta_{g(t)}u(t)$ and the local curvature estimates for the Ricci-harmonic flow under the condition that the Ricci curvature is bounded along the flow. In the second part these local curvature…

We introduce the notions of `super-Ricci flows' and `Ricci flows' for time-dependent families of metric measure spaces $(X,d_t,m_t)_{t\in I}$. The former property is proven to be stable under suitable space-time versions of mGH-convergence.…

A question about Ricci flow is when the diameters of the manifold under the evolving metrics stay finite and bounded away from 0. Topping \cite{T:1} addresses the question with an upper bound that depends on the $L^{(n-1)/2}$ bound of the…

We provide a conceptual assessment of some aspects of fundamental quantum field theories of gravity in light of foundational aspects of the swampland program. On the one hand, asymptotically safe quantum gravity may provide a simple and…