Instanton Partons in 5-dim SU(N) Gauge Theory

TL;DR

The paper addresses the existence and construction of instanton partons in the 5d $SU(N)$ maximally supersymmetric gauge theory arising from the 6d $A_{N-1}$ (2,0) theory. It develops a framework where instanton partons appear as $1/N$-charged constituents at the intersection of magnetic flux sheets in 5d, and shows how circle and two-torus compactifications with nontrivial Wilson lines lead to a decomposition of calorons into fractional monopoles carrying fractional KK momentum along the compact directions. In the symmetric phase, the partons emerge as nonabelian BPS monopoles with minimal charge, and the paper discusses the explicit charge bases, core scales, and potential connections to ADHM data. These results offer a concrete picture of instanton partons and their role in linking 5d gauge dynamics to the underlying 6d (2,0) theory, while highlighting remaining challenges in fully quantizing the symmetric-phase theory.

Abstract

The circle compactification of the 6-dim (2,0) superconformal theory of $A_{N-1}$ type leads the 5-dim SU(N) maximally supersymmetric gauge theory. Instanton solitons embody Kaluza-Klein modes and are conjectured to be composed of partonic constituents. We realize such a parton of 1/N instanton topological charge at the intersection of magnetic flux sheets. After a further compactification with nontrivial Wilson line expectation value, instantons or calorons have been shown to be split into fundamental monopoles of fractional instanton charge. In the symmetric phase with trivial Wilson line expectation value, BPS instanton partons emerge more concretely as nonabelian BPS monopoles of minimum charge allowed in Dirac quantization.