Pure 𝑆𝑈(2) gauge theory partition function and generalized Bessel kernel

2018 ◽  
pp. 181-205 ◽  
Author(s):  
P. Gavrylenko ◽  
O. Lisovyy
Keyword(s):  
Gauge Theory ◽  
Partition Function ◽  
Bessel Kernel

scholarly journals The ABCDEFG of little strings

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Nathan Haouzi ◽  
Can Kozçaz
Keyword(s):  
Gauge Theory ◽  
Partition Function ◽  
Coulomb Gas ◽  
Conformal Block ◽  
Coulomb Branch ◽  
Quiver Gauge Theory ◽  
Codimension Two ◽  
Type Iib String Theory ◽  
Unified Description ◽  
Formula Type

Abstract Starting from type IIB string theory on an ADE singularity, the (2, 0) little string arises when one takes the string coupling gs to 0. In this setup, we give a unified description of the codimension-two defects of the little string, labeled by a simple Lie algebra $$ \mathfrak{g} $$ g . Geometrically, these are D5 branes wrapping 2-cycles of the singularity, subject to a certain folding operation when the algebra is non simply-laced. Equivalently, the defects are specified by a certain set of weights of $$ {}^L\mathfrak{g} $$ L g , the Langlands dual of $$ \mathfrak{g} $$ g . As a first application, we show that the instanton partition function of the $$ \mathfrak{g} $$ g -type quiver gauge theory on the defect is equal to a 3-point conformal block of the $$ \mathfrak{g} $$ g -type deformed Toda theory in the Coulomb gas formalism. As a second application, we argue that in the (2, 0) CFT limit, the Coulomb branch of the defects flows to a nilpotent orbit of $$ \mathfrak{g} $$ g .

scholarly journals On the quantization of Seiberg-Witten geometry

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Nathan Haouzi ◽  
Jihwan Oh
Keyword(s):  
Gauge Theory ◽  
String Theory ◽  
Partition Function ◽  
Flat Space ◽  
Matter Content ◽  
Gauge Groups ◽  
Space Limit ◽  
Two Parameters ◽  
Double Quantization ◽  
Quantization Parameters

Abstract We propose a double quantization of four-dimensional $$ \mathcal{N} $$ N = 2 Seiberg-Witten geometry, for all classical gauge groups and a wide variety of matter content. This can be understood as a set of certain non-perturbative Schwinger-Dyson identities, following the program initiated by Nekrasov [1]. The construction relies on the computation of the instanton partition function of the gauge theory on the so-called Ω-background on ℝ4, in the presence of half-BPS codimension 4 defects. The two quantization parameters are identified as the two parameters of this background. The Seiberg-Witten curve of each theory is recovered in the flat space limit. Whenever possible, we motivate our construction from type IIA string theory.

Chern–Simons gauge theory and symplectic quantum mechanics

2015 ◽  
Vol 93 (9) ◽  
pp. 971-973
Author(s):  
Lisa Jeffrey
Keyword(s):  
Quantum Mechanics ◽  
Gauge Theory ◽  
Partition Function ◽  
Partition Functions ◽  
Action Functional ◽  
Symplectic Action ◽  
Chern Simons

We describe the relation between the Chern–Simons gauge theory partition function and the partition function defined using the symplectic action functional as the Lagrangian. We show that the partition functions obtained using these two Lagrangians agree, and we identify the semiclassical formula for the partition function defined using the symplectic action functional. We also compute the semiclassical formulas for the partition functions obtained using the two different Lagrangians: the Chern–Simons functional and the symplectic action functional.

β-DEFORMED MATRIX MODELS AND NEKRASOV PARTITION FUNCTION

2013 ◽  
Vol 21 ◽  
pp. 92-100
Author(s):  
TAKESHI OOTA
Keyword(s):  
Gauge Theory ◽  
Partition Function ◽  
Matrix Models ◽  
Matrix Model ◽  
The Matrix

The β-deformed matrix models of Selberg type are introduced. They are exactly calculable by using the Macdonald-Kadell formula. With an appropriate choice of the integration contours and interactions, the partition function of the matrix model can be identified with the Nekrasov partition function for SU(2) gauge theory with Nf = 4. Known properties of good q-expansion basis for the matrix model are summarized.

scholarly journals Character Expansion, Zeroes of Partition Function and  -Term in U(1) Gauge Theory

1995 ◽  
Vol 94 (5) ◽  
pp. 861-871 ◽  
Author(s):  
A. S. Hassan ◽  
M. Imachi ◽  
N. Tsuzuki ◽  
H. Yoneyama
Keyword(s):  
Gauge Theory ◽  
Partition Function

scholarly journals ϵ-CORRECTED SEIBERG–WITTEN PREPOTENTIAL OBTAINED FROM HALF-GENUS EXPANSION IN β-DEFORMED MATRIX MODEL

2011 ◽  
Vol 26 (20) ◽  
pp. 3439-3467 ◽  
Author(s):  
H. ITOYAMA ◽  
N. YONEZAWA
Keyword(s):  
Free Energy ◽  
Supersymmetric Gauge Theory ◽  
Gauge Theory ◽  
Partition Function ◽  
Matrix Model ◽  
Conformal Block ◽  
Supersymmetric Gauge ◽  
Genus Expansion ◽  
Resolvent Function ◽  
Explicit Expressions

We consider the half-genus expansion of the resolvent function in the β-deformed matrix model with three-Penner potential under the AGT conjecture and the 0d–4d dictionary. The partition function of the model, after the specification of the paths, becomes the DF conformal block for fixed c and provides the Nekrasov partition function expanded both in [Formula: see text] and in ϵ = ϵ1+ϵ2. Exploiting the explicit expressions for the lower terms of the free energy extracted from the above expansion, we derive the first few ϵ corrections to the Seiberg–Witten prepotential in terms of the parameters of SU(2), Nf = 4, [Formula: see text] supersymmetric gauge theory.

(q, t) identities and vertex operators

2016 ◽  
Vol 31 (11) ◽  
pp. 1650065 ◽  
Author(s):  
Amer Iqbal ◽  
Babar A. Qureshi ◽  
Khurram Shabbir
Keyword(s):  
Gauge Theory ◽  
Partition Function ◽  
Gauge Theories ◽  
Fock Space ◽  
Vertex Operators ◽  
Product Representation ◽  
Modular Transformation ◽  
Exact Product

Using vertex operators acting on fermionic Fock space we prove certain identities, which depend on a number of parameters, generalizing and refining the Nekrasov–Okounkov identity. These identities provide exact product representation for the instanton partition function of certain five-dimensional quiver gauge theories. This product representation also clearly displays the modular transformation properties of the gauge theory partition function.

scholarly journals ON THE HOLOMORPHICALLY FACTORIZED PARTITION FUNCTION FOR ABELIAN GAUGE THEORY IN SIX DIMENSIONS

2002 ◽  
Vol 17 (03) ◽  
pp. 383-393 ◽  
Author(s):  
ANDREAS GUSTAVSSON
Keyword(s):  
Gauge Theory ◽  
Partition Function ◽  
Gauge Field ◽  
Hamiltonian Formulation ◽  
Partition Functions ◽  
Modular Invariant ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
Six Dimensions ◽  
The One

We use holomorphic factorization to find the partition functions of an Abelian two-form chiral gauge-field on a flat six-torus. We prove that exactly one of these partition functions is modular invariant. It turns out to be the one that previously has been found in a Hamiltonian formulation.

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