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.
Doubly Periodic Instanton Zero Modes
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abstract
Fermionic zero modes associated with doubly periodic SU(2) instantons of unit charge are considered. In cases where the action density exhibits two `instanton cores' the zero mode peaks on one of four line-segments joining the two constituents. Which of the four possibilities is realised depends on the fermionic boundary conditions; doubly periodic, doubly anti-periodic or mixed.
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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.