scholarly journals Large N techniques for Nekrasov partition functions and AGT conjecture

2013 ◽  
Vol 2013 (5) ◽  
Author(s):  
Jean-Emile Bourgine
Keyword(s):  
Partition Functions ◽  
Large N ◽  
Nekrasov Partition Functions

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 WILSON LOOPS IN 2D YANG-MILLS: EULER CHARACTERS AND LOOP EQUATIONS

1996 ◽  
Vol 11 (21) ◽  
pp. 3885-3933 ◽  
Author(s):  
SANJAYE RAMGOOLAM
Keyword(s):  
Lattice Models ◽  
Symmetric Groups ◽  
Linear Constraints ◽  
Partition Functions ◽  
Wilson Loops ◽  
Dimensional Lattice ◽  
Yang Mills ◽  
Branched Covering ◽  
Large N ◽  
Higher Dimensional

We give a simple diagrammatic algorithm for writing the chiral large N expansion of intersecting Wilson loops in 2D SU(N) and U(N) Yang-Mills theory in terms of symmetric groups, generalizing the result of Gross and Taylor for partition functions. We prove that these expansions compute Euler characters of a space of branched covering maps from string worldsheets with boundaries. We prove that the Migdal-Makeenko equations hold for the chiral theory and show that they can be expressed as linear constraints on perturbations of the chiral YM 2 partition functions. We briefly discuss finite N, the nonchiral expansion, and higher-dimensional lattice models.

scholarly journals ON THE STRING ACTIONS FOR THE GENERALIZED TWO-DIMENSIONAL YANG-MILLS THEORIES

1996 ◽  
Vol 11 (20) ◽  
pp. 1675-1685 ◽  
Author(s):  
YUJI SUGAWARA
Keyword(s):  
Topological String ◽  
String Model ◽  
Partition Functions ◽  
Two Dimensional ◽  
Yang Mills ◽  
Large N

We study the structures of partition functions of the large-N generalized two-dimensional Yang-Mills theories (gY M2) by recasting the higher Casimirs. We clarify the appropriate interpretations of them and try to extend the Cordes-Moore-Ramgoolam’s topological string model describing the ordinary4Y M2 to those describing gY M2. We present the expressions of the appropriate operators to reproduce the higher Casimir terms in gY M2. The concept of “deformed gravitational descendants” will be introduced for this purpose.

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 UNIVERSAL ASPECTS OF TWO-DIMENSIONAL YANG-MILLS THEORY AT LARGE N

1996 ◽  
Vol 11 (10) ◽  
pp. 1733-1746 ◽  
Author(s):  
MICHAEL CRESCIMANNO ◽  
HOWARD J. SCHNITZER
Keyword(s):  
Functional Form ◽  
Weak Coupling Limit ◽  
Phase Portraits ◽  
Partition Functions ◽  
Two Dimensional ◽  
Fundamental Representation ◽  
Third Order ◽  
Expectation Value ◽  
Yang Mills ◽  
Large N

We show that the large N partition functions and Wilson loop observables of two-dimensional Yang-Mills theories admit a universal functional form irrespective of the gauge group. We demonstrate that U(N) QCD 2 undergoes a large N, third order phase transition on the projective plane at an area coupling product of π2/2. We use this as a lemma to provide a direct transcription for the partition functions and phase portraits of Yang-Mills theory from the U(N) on RP 2 at large N to the other classical Lie groups on S2. We compute the expectation value of the Wilson loops in the fundamental representation for SO (N) and Sp (N) on the two-sphere. Finally we compare the strong and weak coupling limit of these expressions with those found elsewhere in the literature.

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