QuasiHopf twist and elliptic Nekrasov factor
Abstract
We investigate the quasiHopf twist of the quantum toroidal algebra of gl_{1} as an elliptic deformation. Under the quasiHopf 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 quasiHopf 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 &R;^{4}× T^{2}. The same R matrix also appears in the commutation relation of the intertwiners, which implies an elliptic quantum KZ equation for the trace of intertwiners. We also show that it allows a solution which is factorized into the elliptic Nekrasov factors and the triple elliptic gamma function.
 Publication:

Journal of High Energy Physics
 Pub Date:
 December 2021
 DOI:
 10.1007/JHEP12(2021)130
 arXiv:
 arXiv:2110.03970
 Bibcode:
 2021JHEP...12..130C
 Keywords:

 Conformal and W Symmetry;
 Conformal Field Theory;
 Quantum Groups;
 Supersymmetric Gauge Theory;
 High Energy Physics  Theory;
 Mathematical Physics;
 Mathematics  Quantum Algebra;
 Mathematics  Representation Theory
 EPrint:
 45 pages, 3 figures