ADHM/Nahm Construction of Localized Solitons in Noncommutative Gauge Theories

TL;DR

This paper explores the connection between ADHM/Nahm construction and solution generating techniques for creating exact localized BPS solitons in noncommutative gauge theories, introducing new soliton types and clarifying their relationships.

Contribution

It demonstrates how ADHM/Nahm construction naturally produces localized solitons, including new periodic instantons and fluxons, linking different methods and soliton types in noncommutative gauge theories.

Findings

Constructed various exact localized solitons, including new localized calorons and doubly-periodic instantons.

Showed that Nahm construction yields BPS fluxons directly from Nahm data.

Established the equivalence between the Fourier transform of localized calorons and BPS fluxons.

Abstract

We study the relationship between ADHM/Nahm construction and ``solution generating technique'' of BPS solitons in noncommutative gauge theories. ADHM/Nahm construction and ``solution generating technique'' are the most strong ways to construct exact BPS solitons. Localized solitons are the solitons which are generated by the ``solution generating technique.'' The shift operators which play crucial roles in ``solution generating technique'' naturally appear in ADHM/Nahm construction and we can construct various exact localized solitons including new solitons: localized periodic instantons (=localized calorons) and localized doubly-periodic instantons. Nahm construction also gives rise to BPS fluxons straightforwardly from the appropriate input Nahm data which is expected from the D-brane picture of BPS fluxons. We also show that the Fourier-transformed soliton of the localized caloron in the zero-period limit exactly coincides with the BPS fluxon.