BPS Monopoles and Open Spin Chains

We construct SU(n+1) BPS spherically symmetric monopoles with minimal symmetry breaking by solving the full Weyl equation. In this context, we explore and discuss the existence of open spin chain-like part within the Weyl equation. For instance, in the SU(3) case the relevant spin chain is the 2-site spin 1/2 XXX chain with open boundary conditions. We exploit the existence of such a spin chain part in order to solve the full Weyl equation.

💡 Research Summary

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The paper tackles the construction of spherically symmetric BPS monopoles in an SU(n + 1) gauge theory under the condition of minimal symmetry breaking. Traditionally, such monopoles are described via the ADHMN (Nahm) construction, which reduces the problem to solving Nahm’s equations for a set of matrix‑valued functions (T_i(s)) and then solving the associated Weyl equation for the monopole’s Higgs field and gauge potential. In the spherically symmetric, minimally broken case the Nahm data simplify dramatically: (T_i(s)=\frac{1}{s}J_i), where (J_i) generate an (n + 1)‑dimensional representation of SU(2). The remaining task is to solve the full Weyl equation
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