BPS Z(2) monopoles and N=2 SU(n) superconformal field theories on the Higgs branch

TL;DR

This paper constructs BPS Z(2) monopole solutions in SU(n) gauge theories, relates their properties to algebraic weights, and connects these monopoles to vacua in N=2 superconformal field theories, exploring their dualities.

Contribution

It introduces explicit BPS Z(2) monopole solutions in SU(n) theories and links their existence to vacua in N=2 superconformal field theories, revealing new duality insights.

Findings

Fundamental Z(2) monopoles correspond to weights of the dual algebra.

Masses of nonfundamental monopoles equal sums of fundamental monopole masses.

Vacua for Z(2) monopoles are present in the Higgs branch of N=2 superconformal theories.

Abstract

We obtain BPS Z(2) monopole solutions in Yang-Mills-Higgs theories with the gauge group SU(n) broken to Spin(n)/Z(2) by a scalar field in the nxn representation. We show that the magnetic weights of the so-called fundamental Z(2) monopoles correspond to the weights of the defining representation of the algebra dual to so(n), and the masses of the nonfundamental BPS Z(2) monopoles are equal to the sum of the masses of the constituent fundamental monopoles. We also show that the vacua responsible for the existence of these Z(2) monopoles are present in the Higgs branch of a class of N=2 SU(n) superconformal field theories. We analyze some dualities these monopoles may satisfy.