Kavli Affiliate: Masahito Yamazaki
| First 5 Authors: Jiakang Bao, Masahito Yamazaki, , ,
| Summary:
We construct statistical mechanical models of crystal melting describing the
flavoured Witten indices of $mathcal{N}ge 2$ supersymmetric quiver gauge
theories. Our results can be derived from the Jeffrey-Kirwan (JK) residue
formulas, and generalize the previous results for quivers corresponding to
toric Calabi-Yau threefolds and fourfolds to a large class of quivers
satisfying the no-overlap condition, including those corresponding to some
non-toric Calabi-Yau manifolds. We construct new quiver algebras which we call
the double quiver Yangians/algebras, as well as their representations in terms
of the aforementioned crystals. For theories with four supercharges, we compare
the double quiver algebras with the existing quiver Yangians/BPS algebras,
which we show can also be constructed from the JK residues. For theories with
two supercharges, the double quiver algebras provide an algebraic description
of the BPS states, including the information of the fixed points and their
relative coefficients in the full partition functions.
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