β-Ensembles for Toric Orbifold Partition Function

@article{Kimura2011EnsemblesFT,
  title={$\beta$-Ensembles for Toric Orbifold Partition Function},
  author={Taro Kimura},
  journal={Progress of Theoretical Physics},
  year={2011},
  volume={127},
  pages={271-285}
}
  • Taro Kimura
  • Published 31 August 2011
  • Mathematics
  • Progress of Theoretical Physics
We investigate combinatorics of the instanton partition function for the generic four dimensional toric orbifolds. It is shown that the orbifold projection can be implemented by taking the inhomogeneous root of unity limit of the q-deformed partition function. The asymptotics of the combinatorial partition function yields the multi-matrix model for a generic β. Subject Index: 135, 183 

Figures from this paper

Virasoro constraint for Uglov matrix model
Abstract We study the root of unity limit of (q,t)-deformed Virasoro matrix models, for which we call the resulting model Uglov matrix model. We derive the associated Virasoro constraints on the
Twisted reduction of quiver W-algebras
We consider the $k$-twisted Nekrasov-Shatashvili limit (NS$_k$ limit) of 5d (K-theoretic) and 6d (elliptic) quiver gauge theory, where one of the multiplicative equivariant parameters is taken to be
Provisional chapter Gauge Theory , Combinatorics , and Matrix Models
Quantum field theory is the most universal method in physics, applied to all the area from condensed-matter physics to high-energy physics. The standard tool to deal with quantum field theory is the
Fractional quiver W-algebras
We introduce quiver gauge theory associated with the non-simply laced type fractional quiver and define fractional quiver W-algebras by using construction of Kimura and Pestun (Lett Math Phys, 2018.
Gauge Theory, Combinatorics, and Matrix Models
Quantum field theory is the most universal method in physics, applied to all the area from condensed-matter physics to high-energy physics. The standard tool to deal with quantum field theory is the
Spinless basis for spin-singlet FQH states
We investigate an alternative description of the SU(M)-singlet FQH state by using the spinless basis. The SU(M)-singlet Halperin state is obtained via the q-deformation of the Laughlin state and its
Quiver Gauge Theory
  • Taro Kimura
  • Physics
    Instanton Counting, Quantum Geometry and Algebra
  • 2021
Together with a set of edges (arrows) \(\Gamma _1\), we define a quiver \(\Gamma = (\Gamma _0, \Gamma _1)\). For each edge \(e:i \rightarrow j\), in 4d \(\mathcal {N} = 1\) gauge theory (4 SUSY)
Bases in coset conformal field theory from AGT correspondence and Macdonald polynomials at the roots of unity
A bstractWe continue our study of the AGT correspondence between instanton counting on $ {{{{{\mathbb{C}}^2}}} \left/ {{{{\mathbb{Z}}_p}}} \right.} $ and Conformal field theories with the symmetry
Matrix model from $ \mathcal{N} = 2 $ orbifold partition function
The orbifold generalization of the partition function, which would describe the gauge theory on the ALE space, is investigated from the combinatorial perspective. It is shown that the root of unity
Instanton Counting, Quantum Geometry and Algebra
The aim of this memoir for “Habilitation à Diriger des Recherches” is to present quantum geometric and algebraic aspects of supersymmetric gauge theory, which emerge from non-perturbative nature of
...
...

References

SHOWING 1-10 OF 52 REFERENCES
Instantons on ALE spaces and orbifold partitions
We consider = 4 theories on ALE spaces of Ak−1 type. As is well known, their partition functions coincide with Ak−1 affine characters. We show that these partition functions are equal to the
Vortices on orbifolds
The Abelian and non-Abelian vortices on orbifolds are investigated based on the moduli matrix approach, which is a powerful method to deal with the BPS equation. The moduli space and the vortex
S ep 2 01 1 RIKEN-MP-21 Matrix model from N = 2 orbifold partition function
The orbifold generalization of the partition function, which would describe the gauge theory on the ALE space, is investigated from the combinatorial perspective. It is shown that the root of unity
Seiberg-Witten theory and random partitions
We study \( \mathcal{N} = 2 \) supersymmetric four-dimensional gauge theories, in a certain 525-02 = 2 supergravity background, called theΩ-background. The partition function of the theory in the
Liouville Correlation Functions from Four-Dimensional Gauge Theories
We conjecture an expression for the Liouville theory conformal blocks and correlation functions on a Riemann surface of genus g and n punctures as the Nekrasov partition function of a certain class
Instanton counting with a surface operator and the chain-saw quiver
We describe the moduli space of SU(N) instantons in the presence of a general surface operator of type N = n1 + ⋯ + nM in terms of the representations of the so-called chain-saw quiver, which allows
The Nekrasov Conjecture for Toric Surfaces
The Nekrasov conjecture predicts a relation between the partition function for N = 2 supersymmetric Yang–Mills theory and the Seiberg-Witten prepotential. For instantons on $${\mathbb{R}^4}$$, the
Central charges of Liouville and Toda theories from M5-branes.
We show that the central charge of the Liouville and Toda theories of type A, D, and E can be reproduced by equivariantly integrating the anomaly eight-form of the corresponding six-dimensional
A quantum deformation of the Virasoro algebra and the Macdonald symmetric functions
A quantum deformation of the Virasoro algebra is defined. The Kac determinants at arbitrary levels are conjectured. We construct a bosonic realization of the quantum deformed Virasoro algebra.
Multi instanton calculus on ALE spaces
...
...