Non-Commutative Instantons and the Information Metric

TL;DR

This paper explores the geometry of the moduli space of non-commutative instantons using the Information Metric, revealing a correspondence with D-instanton moduli in a five-dimensional spacetime with a B-field, at first order in non-commutativity.

Contribution

It demonstrates how the Information Metric on non-commutative instanton moduli space recovers five-dimensional spacetime and D-instanton moduli correspondence at first order in non-commutativity.

Findings

Recovered five-dimensional spacetime with a B-field using the Information Metric.

Established the correspondence between YM-instanton moduli and D-instanton moduli.

Validated the match at first order of the non-commutativity parameter.

Abstract

By using the so-called Information Metric on the moduli space of an anti-selfdual (ASD) Instanton in a Self-Dual (SD) Non-Commutative background, we investigate the geometry of moduli space. The metric is evaluated perturbatively in non-commutativity parameter and we show that by putting a cut-off in the location of instanton in the definition of Information Metric we can recover the five dimensional space time in the presence of a B-field. This result shows that the non-commutative YM-Instanton Moduli corresponds to D-Instanton Moduli in the gravity side where the radial and transverse location of D-Instanton are corresponding to YM-Instanton size and location, respectively. The match is shown in the first order of non-commutativity parameter.