ADHM/Nahm Construction of Localized Solitons in Noncommutative Gauge Theories

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.” In “solution generating technique,” shift operators play crucial roles. We determine where the shift operators appear in ADHM/Nahm construction and 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 Fouriertransformed soliton of the localized caloron in the zero-period limit exactly coincides with the BPS fluxon. e-mail: [email protected] The author stays at YITP as an atom-type visitor from August 27 to September 20, 2001.