Encoding nontrivial BPS weights in crystal-state labels

Develop an enriched crystal-state formalism that incorporates the nontrivial fugacity-dependent coefficients of two-supercharge partition functions into the state labels and use it to construct representations of the double quiver algebras or new BPS algebras.

Background

For theories with two supercharges, crystal configurations identify fixed points but do not by themselves encode the full BPS counting, because the coefficients are nontrivial rational functions of fugacities. The double quiver algebras retain this information in the coefficients of their actions, but the paper asks whether these data can instead be incorporated directly into enriched state labels and interpreted in terms of BPS charges under the flavor symmetries.