Instanton approximation, periodic ASD connections, and mean dimension

TL;DR

This paper investigates the structure of the moduli space of ASD connections over $S^3 imes R$, including infinite energy cases, by establishing bounds on its mean dimension through approximation and deformation techniques.

Contribution

It introduces a novel analysis of the mean dimension of an infinite dimensional moduli space of ASD connections, extending understanding beyond finite energy cases.

Findings

Upper bound on mean dimension via Runge-approximation

Lower bound established through deformation theory

Infinite dimensional moduli space characterized

Abstract

We study a moduli space of ASD connections over $S^3\times \mathbb{R}$. We consider not only finite energy ASD connections but also infinite energy ones. So the moduli space is infinite dimensional in general. We study the (local) mean dimension of this infinite dimensional moduli space. We show the upper bound on the mean dimension by using a "Runge-approximation" for ASD connections, and we prove its lower bound by constructing an infinite dimensional deformation theory of periodic ASD connections.