Monopoles and instantons on partially compactifiedD-branes

Abstract

Motivated by the recent D-brane constructions of world-volume monopoles and instantons, we study the supersymmetric SU (N ) Yang-Mills theory on S 1 × R 3+1 , spontaneously broken by a Wilson loop. In addition to the usual N −1 fundamental monopoles, the N -th BPS monopole appears from the Kaluza-Klein sector. When all N monopoles are present, net magnetic charge vanishes and the solution can be reinterpreted as a Wilson-loop instanton of unit Pontryagin number. The instanton/multi-monopole moduli space is explicitly constructed, and seen to be identical to a Coulomb phase moduli space of a U (1) N gauge theory in 2 + 1 dimensions related to Kronheimer's gauge theory of SU (N ) type. This extends the results by Intriligator and Seiberg to the finite couplings that, in the infrared limit of Kronheimer's theory, the Coulomb phase parameterizes a centered SU (N ) instanton. We also elaborate on the case of restored SU (N ) symmetry.

Nonperturbative Superpotentials and Compactification to Three Dimensions

“…In addition to the monopoles that contributed to (16), there is one more non-trivial gauge field configuration that contributes, which is the Kaluza-Klein monopole. This is present due to the existence of large gauge transformations along the S 1 [35].…”

Instantons at work

“…Therefore these objects carry both electric and magnetic charges. In the 3+1-dimensional SU(2) gauge theory there are in fact two types of self-dual dyons [48]: M and L with (electric, magnetic) charges (+, +) and (−, −), and two types of anti-self-dual dyonsM andL with charges (+, −) and (−, +), respectively. Their explicit fields can be found e.g.…”

Instantons and magnetic monopoles on R3×S1 with arbitrary simple gauge groups

“…In recent years there has been some interest in the connection between magnetic monopoles and instantons in theories with partially compactified space [1,2,3]. Especially by employing the Tduality on D-branes, we have shown that a single instanton in the theory with SU n gauge group on space R 3 × S 1 can be interpreted as a composite of n distinct fundamental monopoles [1].…”