# 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}
}
• Published 8 October 2021
• Mathematics
• Journal of High Energy Physics
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…

## References

SHOWING 1-10 OF 78 REFERENCES
Quasi-Hopf twistors for elliptic quantum groups
• Mathematics
• 1997
AbstractThe Yang-Baxter equation admits two classes of elliptic solutions, the vertex type and the face type. On the basis of these solutions, two types of elliptic quantum groups have been
A commutative algebra on degenerate CP^1 and Macdonald polynomials
• Mathematics
• 2009
We introduce a unital associative algebra A over degenerate CP^1. We show that A is a commutative algebra and whose Poincar'e series is given by the number of partitions. Thereby we can regard A as a
Elliptic Algebra : Drinfeld Currents and Vertex Operators
• Mathematics
• 1998
Abstract:We investigate the structure of the elliptic algebra introduced earlier by one of the authors. Our construction is based on a new set of generating series in the quantum affine algebra ,
Drinfeld realization of the elliptic Hall algebra
We give a new presentation of the Drinfeld double $\boldsymbol{\mathcal {E}}$ of the (spherical) elliptic Hall algebra $\boldsymbol{\mathcal{E}}^{+}$ introduced in our previous work (Burban and
An elliptic Virasoro symmetry in 6d
It is proposed that at special points in the moduli space the 6d Nekrasov partition function reduces to the partition function of a 4d vortex theory supported on R2×T2, which is in turn captured by a free field correlator of vertex operators and screening charges of the elliptic Virasoro algebra.
Quantum affine algebras and holonomic difference equations
• Mathematics
• 1992
AbstractWe derive new holonomicq-difference equations for the matrix coefficients of the products of intertwining operators for quantum affine algebra representations of levelk. We study the
On the Hall algebra of an elliptic curve, I
• Mathematics
• 2005
This paper is a sequel to math.AG/0505148, where the Hall algebra U^+_E of the category of coherent sheaves on an elliptic curve E defined over a finite field was explicitly described, and shown to
Elliptic modular double and 4d partition functions
• Mathematics
• 2017
We consider 4d supersymmetric (special) unitary $\Gamma$ quiver gauge theories on compact manifolds which are $T^2$ fibrations over $S^2$. We show that their partition functions are correlators of
Matrix models, geometric engineering and elliptic genera
• Mathematics
• 2008
We compute the prepotential of = 2 supersymmetric gauge theories in four dimensions obtained by toroidal compactifications of gauge theories from 6 dimensions, as a function of Kahler and complex
Quantum algebraic approach to refined topological vertex
• Mathematics
• 2011
A bstractWe establish the equivalence between the refined topological vertex of Iqbal-Kozcaz-Vafa and a certain representation theory of the quantum algebra of type W1+∞ introduced by Miki. Our