Explicit theta-function solutions for fractional BPS lumps on a twisted torus are constructed, and the moduli space is a CP^(Nk+p-1) fiber bundle over a small torus, matching the index theorem.
Monopoles in the Higgs Phase
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abstract
We describe new solutions of Yang-Mills-Higgs theories consisting of magnetic monopoles in a phase with fully broken gauge symmetry. Rather than spreading out radially, the magnetic field lines form flux tubes. The solution is topologically stable and, when embedded in N=2 SQCD, preserves 1/4 of the supercharges. From the perspective of the flux-tube the monopole appears as a kink. Many monopoles may be threaded onto a single flux tube and placed at arbitrary separation to create a stable, BPS necklace of solitons.
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Fractional instantons in 2d $\mathbb{C}P^{N-1}$ model and 4d Yang-Mills theory with 't Hooft twists
Explicit theta-function solutions for fractional BPS lumps on a twisted torus are constructed, and the moduli space is a CP^(Nk+p-1) fiber bundle over a small torus, matching the index theorem.