scholarly journals Calculating the partition function of $ \mathcal{N} = 2 $ gauge theories on S 3 and AdS/CFT correspondence

2011 ◽  
Vol 2011 (5) ◽  
Author(s):  
Sangmo Cheon ◽  
Hyojoong Kim ◽  
Nakwoo Kim
Keyword(s):  
Partition Function ◽  
Gauge Theories

scholarly journals Gauge theories on compact toric manifolds

2021 ◽  
Vol 111 (3) ◽  
Author(s):  
Giulio Bonelli ◽  
Francesco Fucito ◽  
Jose Francisco Morales ◽  
Massimiliano Ronzani ◽  
Ekaterina Sysoeva ◽  
...  
Keyword(s):  
Partition Function ◽  
Gauge Theories ◽  
Blow Up ◽  
Gauge Coupling ◽  
Piecewise Constant Function ◽  
Partition Functions ◽  
Piecewise Constant ◽  
Toric Manifolds ◽  
Holomorphic Anomaly ◽  
The One

AbstractWe compute the $$\mathcal{N}=2$$ N = 2 supersymmetric partition function of a gauge theory on a four-dimensional compact toric manifold via equivariant localization. The result is given by a piecewise constant function of the Kähler form with jumps along the walls where the gauge symmetry gets enhanced. The partition function on such manifolds is written as a sum over the residues of a product of partition functions on $$\mathbb {C}^2$$ C 2 . The evaluation of these residues is greatly simplified by using an “abstruse duality” that relates the residues at the poles of the one-loop and instanton parts of the $$\mathbb {C}^2$$ C 2 partition function. As particular cases, our formulae compute the SU(2) and SU(3) equivariant Donaldson invariants of $$\mathbb {P}^2$$ P 2 and $$\mathbb {F}_n$$ F n and in the non-equivariant limit reproduce the results obtained via wall-crossing and blow up methods in the SU(2) case. Finally, we show that the U(1) self-dual connections induce an anomalous dependence on the gauge coupling, which turns out to satisfy a $$\mathcal {N}=2$$ N = 2 analog of the $$\mathcal {N}=4$$ N = 4 holomorphic anomaly equations.

scholarly journals MODIFIED PARTITION FUNCTIONS, CONSISTENT ANOMALIES AND CONSISTENT SCHWINGER TERMS

2011 ◽  
Vol 08 (08) ◽  
pp. 1747-1762 ◽  
Author(s):  
AMIR ABBASS VARSHOVI
Keyword(s):  
Partition Function ◽  
Gauge Theories ◽  
Partition Functions ◽  
Gauge Invariant

A gauge invariant partition function is defined for gauge theories which leads to the standard quantization. It is shown that the descent equations and consequently the consistent anomalies and Schwinger terms can be extracted from this modified partition function naturally.

scholarly journals Partition function of N = 2 gauge theories on a squashed S 4 with SU (2)× U (1) isometry

2015 ◽  
Vol 899 ◽  
pp. 149-164 ◽  
Author(s):  
Alejandro Cabo-Bizet ◽  
Edi Gava ◽  
Victor I. Giraldo-Rivera ◽  
M. Nouman Muteeb ◽  
K.S. Narain
Keyword(s):  
Partition Function ◽  
Gauge Theories

Complex zeros of the partition function for lattice gauge theories

1992 ◽  
Vol 26 ◽  
pp. 329-331
Author(s):  
I.M. Barbour ◽  
A.J. Bell ◽  
M. Bernaschi ◽  
G. Salina ◽  
A. Vladikas
Keyword(s):  
Partition Function ◽  
Gauge Theories ◽  
Lattice Gauge ◽  
Lattice Gauge Theories ◽  
Complex Zeros

scholarly journals Black Hole Quasinormal Modes and Seiberg–Witten Theory

2021 ◽  
Author(s):  
Gleb Aminov ◽  
Alba Grassi ◽  
Yasuyuki Hatsuda
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Perturbation Theory ◽  
Partition Function ◽  
Gauge Theories ◽  
Quasinormal Modes ◽  
Spheroidal Harmonics ◽  
Witten Theory ◽  
Supersymmetric Gauge ◽  
Exact Version

AbstractWe present new analytic results on black hole perturbation theory. Our results are based on a novel relation to four-dimensional $${\mathcal {N}}=2$$ N = 2 supersymmetric gauge theories. We propose an exact version of Bohr-Sommerfeld quantization conditions on quasinormal mode frequencies in terms of the Nekrasov partition function in a particular phase of the $$\Omega $$ Ω -background. Our quantization conditions also enable us to find exact expressions of eigenvalues of spin-weighted spheroidal harmonics. We test the validity of our conjecture by comparing against known numerical results for Kerr black holes as well as for Schwarzschild black holes. Some extensions are also discussed.

(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 Topological vertex for 6d SCFTs with ℤ2-twist

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Hee-Cheol Kim ◽  
Minsung Kim ◽  
Sung-Soo Kim
Keyword(s):  
Partition Function ◽  
Gauge Theories ◽  
Outer Automorphism ◽  
Elliptic Genus ◽  
Partition Functions ◽  
Topological Vertex

Abstract We compute the partition function for 6d $$ \mathcal{N} $$ N = 1 SO(2N) gauge theories compactified on a circle with ℤ2 outer automorphism twist. We perform the computation based on 5-brane webs with two O5-planes using topological vertex with two O5-planes. As representative examples, we consider 6d SO(8) and SU(3) gauge theories with ℤ2 twist. We confirm that these partition functions obtained from the topological vertex with O5-planes indeed agree with the elliptic genus computations.

scholarly journals Decomposition of BPS moduli spaces and asymptotics of supersymmetric partition functions

2022 ◽  
Vol 2022 (1) ◽  
Author(s):  
Arash Arabi Ardehali ◽  
Junho Hong
Keyword(s):  
Partition Function ◽  
Moduli Space ◽  
Moduli Spaces ◽  
Gauge Theories ◽  
Asymptotic Expression ◽  
Effective Field ◽  
Asymptotic Result ◽  
Partition Functions ◽  
Abelian Gauge ◽  
Scale Hierarchy

Abstract We present a prototype for Wilsonian analysis of asymptotics of supersymmetric partition functions of non-abelian gauge theories. Localization allows expressing such partition functions as an integral over a BPS moduli space. When the limit of interest introduces a scale hierarchy in the problem, asymptotics of the partition function is obtained in the Wilsonian approach by i) decomposing (in some suitable scheme) the BPS moduli space into various patches according to the set of light fields (lighter than the scheme dependent cut-off Λ) they support, ii) localizing the partition function of the effective field theory on each patch (with cut-offs set by the scheme), and iii) summing up the contributions of all patches to obtain the final asymptotic result (which is scheme-independent and accurate as Λ → ∞). Our prototype concerns the Cardy-like asymptotics of the 4d superconformal index, which has been of interest recently for its application to black hole microstate counting in AdS5/CFT4. As a byproduct of our analysis we obtain the most general asymptotic expression for the index of gauge theories in the Cardy-like limit, encompassing and extending all previous results.

scholarly journals Elliptic lift of the Shiraishi function as a non-stationary double-elliptic function

2020 ◽  
Vol 2020 (8) ◽  
Author(s):  
Hidetoshi Awata ◽  
Hiroaki Kanno ◽  
Andrei Mironov ◽  
Alexei Morozov
Keyword(s):  
Partition Function ◽  
Elliptic Function ◽  
Gauge Theories ◽  
Network Models ◽  
Symmetric Polynomials ◽  
Conformal Blocks ◽  
Gamma Functions ◽  
Elliptic Genera ◽  
Surface Operator ◽  
Insufficient Number

Abstract As a development of [1], we note that the ordinary Shiraishi functions have an insufficient number of parameters to describe generic eigenfunctions of double elliptic system (Dell). The lacking parameter can be provided by substituting elliptic instead of the ordinary Gamma functions in the coefficients of the series. These new functions (ELS-functions) are conjectured to be functions governed by compactified DIM networks which can simultaneously play the three roles: solutions to non-stationary Dell equations, Dell conformal blocks with the degenerate field (surface operator) insertion, and the corresponding instanton sums in 6d SUSY gauge theories with adjoint matter. We describe the basics of the corresponding construction and make further conjectures about the various limits and dualities which need to be checked to make a precise statement about the Dell description by double-periodic network models with DIM symmetry. We also demonstrate that the ELS-functions provide symmetric polynomials, which are an elliptic generalization of Macdonald ones, and compute the generation function of the elliptic genera of the affine Laumon spaces. In the particular U(1) case, we find an explicit plethystic formula for the 6d partition function, which is a non-trivial elliptic generalization of the (q, t) Nekrasov-Okounkov formula from 5d.

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