Weyl Equation and (Non)-Commutative SU(n+1) BPS Monopoles

TL;DR

This paper constructs spherically symmetric BPS monopoles for SU(n+1) gauge groups using the ADHMN method, solving the Weyl equation with special functions, and extends the approach to non-commutative cases with Heun functions.

Contribution

It provides explicit solutions for SU(n+1) BPS monopoles and generalizes the construction to non-commutative gauge theories using special functions.

Findings

Explicit solutions for SU(n+1) monopoles using Weyl equations

Extension of monopole solutions to non-commutative spaces

Solutions expressed in terms of Whittaker and Heun functions

Abstract

We apply the ADHMN construction to obtain the SU(n+1)(for generic values of n) spherically symmetric BPS monopoles with minimal symmetry breaking. In particular, the problem simplifies by solving the Weyl equation, leading to a set of coupled equations, whose solutions are expressed in terms of the Whittaker functions. Next, this construction is generalized for non-commutative SU(n+1) BPS monopoles, where the corresponding solutions are given in terms of the Heun B functions.