Related papers: Iterated logarithms and gradient flows
We construct and study the Yang-Mills measure in two dimensions. According to the informal description given by the physicists, it is a probability measure on the space of connections modulo gauge transformations on a principal bundle with…
A framework for constructing new kinds of gauge theories is suggested. Essentially it consists in replacing Lie algebras by Lie or Courant algebroids. Besides presenting novel topological theories defined in arbitrary spacetime dimensions,…
The main results of this paper are limit theorems for horocycle flows on compact surfaces of constant negative curvature. One of the main objects of the paper is a special family of horocycle-invariant finitely-additive Hoelder measures on…
We study modular and integral flow polynomials of graphs by means of subgroup arrangements and lattice polytopes. We introduce an Eulerian equivalence relation on orientations, flow arrangements, and flow polytopes; and we apply the theory…
Let $X$ be a vector field and $Y$ be a co-vector field on a smooth manifold $M$. Does there exist a smooth Riemannian metric $g_{\alpha \beta}$ on $M$ such that $Y_\beta = g_{\alpha \beta} X^\alpha$? The main result of this note gives…
Planar L-loop maximally helicity violating amplitudes in N = 4 supersymmetric Yang-Mills theory are believed to possess the remarkable property of satisfying iteration relations in L. We propose a simple new method for studying the…
We give the global picture of the normalized Ricci flow on generalized flag manifolds with two or three isotropy summands. The normalized Ricci flow for these spaces descents to a parameter depending system of two or three ordinary…
To isolate the multiscale dynamics of the logarithmic layer of wall-bounded turbulent flows, a novel numerical experiment is conducted in which the mean tangential Reynolds stress is eliminated except in a subregion corresponding to the…
A new class of two dimensional integrable field theories, based on the mathematical notion of Poisson manifolds, and containing gravity-Yang-Mills systems as well as the G/G gauged Wess-Zumino Witten-model, are presented. The local…
We revisit the existence of monotonic quantities along renormalization group flows using only the Null Energy Condition and the Ryu-Takayanagi formula for the entanglement entropy of field theories with anti-de Sitter gravity duals. In…
In the present work we find the Lie point symmetries of the Ricci flow on an $n$-dimensional manifold. and we introduce a method in order to reutilize these symmetries to obtain the Lie point symmetries of particular metrics. We apply this…
Flows are exact-likelihood generative neural networks that transform samples from a simple prior distribution to the samples of the probability distribution of interest. Boltzmann Generators (BG) combine flows and statistical mechanics to…
We prove a general criterion to establish existence and uniqueness of a short-time solution to an evolution equation involving "closed" sections of a vector bundle, generalizing a method used recently by Bryant and Xu for studying the…
Asymptotic symmetries of the Einstein-Yang-Mills system with or without cosmological constant are explicitly worked out in a unified manner. In agreement with a recent conjecture, one finds a Virasoro-Kac-Moody type algebra not only in…
Machine-learned normalizing flows can be used in the context of lattice quantum field theory to generate statistically correlated ensembles of lattice gauge fields at different action parameters. This work demonstrates how these…
We establish various existence and uniqueness results for the Yang-Mills flow on cylindrical end 4-manifolds. We also show long-time existence and infinite-time convergence under certain hypotheses on the underlying data.
For the eight-dimensional Riemannian manifold comprised by the three-level quantum systems endowed with the Bures metric, we numerically approximate the integrals over the manifold of several functions of the curvature and of its…
We propose a general framework to extend Flow Matching to homogeneous spaces, i.e. quotients of Lie groups. Our approach reformulates the problem as a flow matching task on the underlying Lie group by lifting the data distributions. This…
This supplementary manuscript is to describe an important nontrivial example, which appears in the matrix model of type IIB in the super string theory in order to apply a new duality for the moduli spaces of Yang-Mills connections on…
A three-layer asymptotic structure for turbulent pipe flow is proposed, revealing in terms of intermediate variables, the existence of a Reynolds-number invariant logarithmic region. It provides a theoretical foundation for addressing…