Space-Time Foam From Non-Commutative Instantons

TL;DR

This paper demonstrates that U(1) instantons on non-commutative R^4 correspond to smooth gauge fields on blown-up Kahler manifolds, linking space-time foam structures with integrable Calogero-Moser systems.

Contribution

It establishes a novel correspondence between non-commutative instantons and smooth gauge fields on blown-up manifolds, connecting space-time foam with integrable systems.

Findings

U(1) instantons correspond to non-singular gauge fields on blown-up manifolds

The manifold X acts as a space-time foam for instanton charge k

A connection with Calogero-Moser integrable systems is established

Abstract

We show that a U(1) instanton on non-commutative R^4 corresponds to a supersymmetric non-singular U(1) gauge field on a commutative Kahler manifold X which is a blowup of C^2 at a finite number of points. For instanton charge k the manifold X can be viewed as a space-time foam. A direct connection with integrable systems of Calogero-Moser type is established. We also make some comments on the non-abelian case.