The variant of ADHMN construction associated with q-analysis
Atsushi Nakamula
TL;DR
This paper introduces a q-deformation of the ADHMN caloron construction, preserving anti-selfdual conditions, and demonstrates its application by constructing a q-deformed Harrington-Shepard caloron, exploring parameter limits.
Contribution
It develops a novel q-deformed ADHMN construction that maintains ASD conditions and applies it to create a new class of q-deformed calorons.
Findings
q-dependent Nahm data are essential for ASD gauge fields
Constructed a q-deformed Harrington-Shepard caloron
Analyzed parameter limits of the q-deformed solutions
Abstract
A q-deformation of the ADHMN caloron construction is considered, under which the anti-selfdual (ASD) conditions of the gauge fields are preserved. It is shown that the q-dependent Nahm data with certain constraints are crucial to determine the ASD gauge fields, as in the case of ordinary caloron construction. As an application of the q-deformed ADHMN construction, we give a q-deformed caloron of Harrington-Shepard type. Some limits of the parameters are also considered.
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