Branes, quivers and wave-functions

We consider a large class of branes in toric strip geometries, both non-periodic and periodic ones. For a fixed background geometry we show that partition functions for such branes can be reinterpreted, on one hand, as quiver generating series, and on the other hand as wave-functions in various polarizations. We determine operations on quivers, as well as SL(2, Z) transformations, which correspond to changing positions of these branes. Our results prove integrality of BPS multiplicities associated to this class of branes, reveal how they transform under changes of polarization, and imply all other properties of brane amplitudes that follow from the relation to quivers.

Automated summary

We investigate a class of branes in toric strip geometries and find that their partition functions can be reinterpreted as quiver generating series and wave-functions in different polarizations. We determine operations on quivers and SL(2, Z) transformations that correspond to changing positions of these branes. Our results confirm the integrality of BPS multiplicities associated with these branes and reveal how they transform under changes in polarization.