scholarly journals (q, t)-KZ equations for quantum toroidal algebra and Nekrasov partition functions on ALE spaces

2018 ◽  
Vol 2018 (3) ◽  
Author(s):  
Hidetoshi Awata ◽  
Hiroaki Kanno ◽  
Andrei Mironov ◽  
Alexei Morozov ◽  
Kazuma Suetake ◽  
...  
Keyword(s):  
Partition Functions ◽  
Toroidal Algebra ◽  
Nekrasov Partition Functions

scholarly journals $$ \mathfrak{gl} $$N Higgsed networks

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Yegor Zenkevich
Keyword(s):  
Lie Algebra ◽  
Partition Functions ◽  
Toroidal Algebra

Abstract We generalize the framework of Higgsed networks of intertwiners to the quantum toroidal algebra associated to Lie algebra $$ \mathfrak{gl} $$ gl N. Using our formalism we obtain a systems of screening operators corresponding to W-algebras associated to toric strip geometries and reproduce partition functions of 3d theories on orbifolded backgrounds.

scholarly journals More on topological vertex formalism for 5-brane webs with O5-plane

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Hirotaka Hayashi ◽  
Rui-Dong Zhu
Keyword(s):  
Gauge Theory ◽  
Partition Function ◽  
Vertex Operator ◽  
Vertex Function ◽  
Gauge Theories ◽  
Partition Functions ◽  
Topological Vertex ◽  
Concrete Form ◽  
Nekrasov Partition Functions ◽  
Chern Simons

Abstract We propose a concrete form of a vertex function, which we call O-vertex, for the intersection between an O5-plane and a 5-brane in the topological vertex formalism, as an extension of the work of [1]. Using the O-vertex it is possible to compute the Nekrasov partition functions of 5d theories realized on any 5-brane web diagrams with O5-planes. We apply our proposal to 5-brane webs with an O5-plane and compute the partition functions of pure SO(N) gauge theories and the pure G2 gauge theory. The obtained results agree with the results known in the literature. We also compute the partition function of the pure SU(3) gauge theory with the Chern-Simons level 9. At the end we rewrite the O-vertex in a form of a vertex operator.

scholarly journals Partition functions of 𝒩 = 1 gauge theories on S2 × ℝ𝜀2 and duality

2020 ◽  
Vol 35 (33) ◽  
pp. 2050207
Author(s):  
Taro Kimura ◽  
Jun Nian ◽  
Peng Zhao
Keyword(s):  
Path Integral ◽  
Gauge Theories ◽  
Building Blocks ◽  
Partition Functions ◽  
Seiberg Duality ◽  
Nekrasov Partition Functions

We compute the partition functions of [Formula: see text] gauge theories on [Formula: see text] using supersymmetric localization. The path integral reduces to a sum over vortices at the poles of [Formula: see text] and at the origin of [Formula: see text]. The exact partition functions allow us to test Seiberg duality beyond the supersymmetric index. We propose the [Formula: see text] partition functions on the [Formula: see text]-background, and show that the Nekrasov partition functions can be recovered from these building blocks.

scholarly journals Gluing Nekrasov Partition Functions

2015 ◽  
Vol 337 (2) ◽  
pp. 785-816 ◽  
Author(s):  
Jian Qiu ◽  
Luigi Tizzano ◽  
Jacob Winding ◽  
Maxim Zabzine
Keyword(s):  
Partition Functions ◽  
Nekrasov Partition Functions

scholarly journals Analyticity of Nekrasov Partition Functions

2018 ◽  
Vol 364 (2) ◽  
pp. 683-718 ◽  
Author(s):  
Giovanni Felder ◽  
Martin Müller-Lennert
Keyword(s):  
Partition Functions ◽  
Nekrasov Partition Functions
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