# Instanton Moduli Spaces and Bases in Coset Conformal Field Theory

@article{Belavin2013InstantonMS, title={Instanton Moduli Spaces and Bases in Coset Conformal Field Theory}, author={Alexander Belavin and M. Bershtein and Boris Feigin and Alexey Vad. Litvinov and Grigory M. Tarnopolsky}, journal={Communications in Mathematical Physics}, year={2013}, volume={319}, pages={269-301} }

The recently proposed relation between conformal field theories in two dimensions and supersymmetric gauge theories in four dimensions predicts the existence of the distinguished basis in the space of local fields in CFT. This basis has a number of remarkable properties: one of them is the complete factorization of the coefficients of the operator product expansion. We consider a particular case of the U(r) gauge theory on $${\mathbb{C}^{2}/\mathbb{Z}_{p}}$$ which corresponds to a certain coset…

## 87 Citations

$ \mathcal{N}=2 $ gauge theories on toric singularities, blow-up formulae and W-algebrae

- Mathematics
- 2012

A bstractWe compute the Nekrasov partition function of gauge theories on the (resolved) toric singularities $ {{{{{\mathbb{C}}^2}}} \left/ {\varGamma } \right.} $ in terms of blow-up formulae. We…

2 D CFT blocks for the 4 D class S k theories

- Mathematics
- 2017

This is the first in a series of papers on the search for the 2D CFT description of a large class of 4D N = 1 gauge theories. Here, we identify the 2D CFT symmetry algebra and its representations,…

Liouville’s imaginary shadow

- Physics
- 2012

A bstract$ \mathcal{N}=1 $ super Liouville field theory is one of the simplest non-rational conformal field theories. It possesses various important extensions and interesting applications, e.g. to…

Isomonodromic deformations and conformal field theory with W-symmetry

- Mathematics
- 2018

The correspondence between isomonodromic deformations and conformal field theories with W-symmetry relates isomonodromic tau-functions to linear combinations of conformal blocks of the W-algebras. In…

Residue formulas for prepotentials, instanton expansions and conformal blocks

- Mathematics
- 2014

A bstractWe study the extended prepotentials for the S-duality class of quiver gauge theories, considering them as quasiclassical tau-functions, depending on gauge theory condensates and bare…

On spectrum of ILW hierarchy in conformal field theory

- Mathematics
- 2013

A bstractWe consider a system of Integrals of Motion in conformal field theory related to the $ \mathfrak{g}\mathfrak{l}(2) $ Intermediate Long Wave equation. It interpolates between the system…

## References

SHOWING 1-10 OF 62 REFERENCES

Super Liouville conformal blocks from $ \mathcal{N} = 2 $ SU(2) quiver gauge theories

- Mathematics, Physics
- 2011

The conjecture about the correspondence between instanton partition functions in the N = 2 SUSY Yang-Mills theory and conformal blocks of two-dimensional conformal field theories is extended to the…

Affine SL(2) Conformal Blocks from 4d Gauge Theories

- Mathematics
- 2010

We study Nekrasov’s instanton partition function of four-dimensional $${\mathcal{N}=2}$$ gauge theories in the presence of surface operators. This can be computed order by order in the instanton…

On Combinatorial Expansion of the Conformal Blocks Arising from AGT Conjecture

- Mathematics
- 2011

In their recent paper, Alday et al. (Lett Math Phys 91:167–197, 2010) proposed a relation between $${\mathcal{N}=2}$$ four-dimensional supersymmetric gauge theories and two-dimensional conformal…

Representations of the algebra of “parafermion currents” of spin 4/3 in two-dimensional conformal field theory. Minimal models and the tricritical potts Z3 model

- Mathematics
- 1987

One of the main tasks of the theory of phase transitions of the second kind is the classification of all possible types of critical behavior together with calculation of the corresponding critical…

Super Liouville conformal blocks from N=2 SU(2) quiver gauge theories

- Mathematics, Physics
- 2011

The conjecture about the correspondence between instanton partition functions in theN = 2 SUSY Yang-Mills theory and conformal blocks of two-dimensi onal conformal field theories is extended to the…

Instanton counting on blowup. I. 4-dimensional pure gauge theory

- Mathematics
- 2003

We give a mathematically rigorous proof of Nekrasov’s conjecture: the integration in the equivariant cohomology over the moduli spaces of instantons on ℝ4 gives a deformation of the Seiberg-Witten…

Instantons on ALE spaces and super Liouville conformal field theories

- Mathematics
- 2011

We provide evidence that the conformal blocks of $ \mathcal{N} = 1 $ super Liouville conformal field theory are described in terms of the SU(2) Nekrasov partition function on the ALE space $…