Quasi-Hopf twist and elliptic Nekrasov factor

@article{Cheewaphutthisakun2021QuasiHopfTA,
  title={Quasi-Hopf twist and elliptic Nekrasov factor},
  author={Panupong Cheewaphutthisakun and Hiroaki Kanno},
  journal={Journal of High Energy Physics},
  year={2021}
}
Abstract We investigate the quasi-Hopf twist of the quantum toroidal algebra of $$ {\mathfrak{gl}}_1 $$ gl 1 as an elliptic deformation. Under the quasi-Hopf twist the underlying algebra remains the same, but the coproduct is deformed, where the twist parameter p is identified as the elliptic modulus. Computing the quasi-Hopf twist of the R matrix, we uncover the relation to the elliptic lift of the Nekrasov factor for instanton counting of the quiver gauge theories on ℝ4× T2. The same… 

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