Abstract
We explore BPS quivers for D = 5 theories, compactified on a circle and geometrically engineered over local Calabi-Yau 3-folds, for which many of known machineries leading to (refined) indices fail due to the fine-tuning of the superpotential. For Abelian quivers, the counting reduces to a geometric one, but the technically challenging L2 cohomology proved to be essential for sensible BPS spectra. We offer a mathematical theorem to remedy the difficulty, but for non-Abelian quivers, the cohomology approach itself fails because the relevant wavefunctions are inherently gauge-theoretical. For the Cartan part of gauge multiplets, which suffers no wall-crossing, we resort to the D0 picture and reconstruct entire KK towers. We also perform numerical checks using a multi-center Coulombic routine, with a simple hypothesis on the quiver invariants, and extend this to electric BPS states in the weak coupling chamber. We close with a comment on known Donaldson-Thomas invariants and on how L2 index might be read off from these.
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Duan, Z., Ghim, D. & Yi, P. 5D BPS quivers and KK towers. J. High Energ. Phys. 2021, 119 (2021). https://doi.org/10.1007/JHEP02(2021)119
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DOI: https://doi.org/10.1007/JHEP02(2021)119