n-th parafermion $$ {\mathcal{W}}_N $$ characters from U(N) instanton counting on ℂ2/ℤn

Manabe, Masahide

doi:10.1007/jhep06(2020)112

Cited by 5 publications

(2 citation statements)

References 65 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The AGT correspondence relates partition functions of class S theories to correlation functions of Toda theory on the compactification surface. There are various generalizations of the correspondence and in [101][102][103][104][105][106] evidence was collected that SU(N ) N = 2 gauge theory on the ALE space C 2 /Z n is related to the Grassmannian coset with µ 1 = n, µ 2 related to the parameter of the Ω-deformation and N = − 1 2 (µ 1 + µ 2 + µ 3 ). We expect that the techniques developed in this paper will be useful for a further study of the correspondence.…”

Section: Jhep09(2020)150mentioning

confidence: 99%

The Grassmannian VOA

Eberhardt

Procházka²

2020

J. High Energ. Phys.

View full text Add to dashboard Cite

We study the 3-parametric family of vertex operator algebras based on the Grassmannian coset CFT $$ \mathfrak{u} $$ u (M + N )k /($$ \mathfrak{u} $$ u (M )k×$$ \mathfrak{u} $$ u (N )k ). This VOA serves as a basic building block for a large class of cosets and generalizes the $$ {\mathcal{W}}_{\infty } $$ W ∞ algebra. We analyze representations and their characters in detail and find surprisingly simple character formulas for the representations in the generic parameter regime that admit an elegant combinatorial formulation. We also discuss truncations of the algebra and give a conjectural formula for the complete set of truncation curves. We develop a theory of gluing for these algebras in order to build more complicated coset and non-coset algebras. We demonstrate the power of this technology with some examples and show in particular that the $$ \mathcal{N} $$ N = 2 supersymmetric Grassmannian can be obtained by gluing three bosonic Grassmannian algebras in a loop. We finally speculate about the tantalizing possibility that this algebra is a specialization of an even larger 4-parametric family of algebras exhibiting pentality symmetry. Specializations of this conjectural family should include both the unitary Grassmannian family as well as the Lagrangian Grassmannian family of VOAs which interpolates between the unitary and the orthosymplectic cosets.

show abstract

Section: Jhep09(2020)150mentioning

confidence: 99%

The Grassmannian VOA

Eberhardt

Procházka²

2020

J. High Energ. Phys.

View full text Add to dashboard Cite

show abstract

“…There are various generalizations of the correspondence and in [101][102][103][104][105][106] evidence was collected that SU(N) N = 2 gauge theory on the ALE space C 2 /Z n is related to the Grassmannian coset with µ 1 = n, µ 2 related to the parameter of the Ω-deformation and N = − 1 2 (µ 1 + µ 2 + µ 3 ). We expect that the techniques developed in this paper will be useful for a further study of the correspondence.…”

Section: Exceptional Algebrasmentioning

confidence: 99%

The Grassmannian VOA

Eberhardt,

Procházka

2020

Preprint

View full text Add to dashboard Cite

We study the 3-parametric family of vertex operator algebras based on the unitary Grassmannian coset CFT u(M +N) k /(u(M) k ×u(N) k ). This VOA serves as a basic building block for a large class of cosets and generalizes the W ∞ algebra. We analyze representations and their characters in detail and find surprisingly simple character formulas for the representations in the generic parameter regime that admit an elegant combinatorial formulation. We also discuss truncations of the algebra and give a conjectural formula for the complete set of truncation curves. We develop a theory of gluing for these algebras in order to build more complicated coset and noncoset algebras. We demonstrate the power of this technology with some examples and show in particular that the N = 2 supersymmetric Grassmannian can be obtained by gluing three bosonic Grassmannian algebras in a loop. We finally speculate about the tantalizing possibility that this algebra is a specialization of an even larger 4parametric family of algebras exhibiting pentality symmetry. Specialization of this conjectural family should include both the unitary Grassmannian family as well as the Lagrangian Grassmannian family of VOAs which interpolates between the unitary and the orthosymplectic cosets. 8 Four-parametric family of algebras 64 9 Discussion and Conclusions 70 A Character background 75 A.1 The cycle index and the Pólya enumeration theorem 75 A.2 Pólya enumeration theorem 75 A.3 The vacuum character of the Grassmannian 76 A.4 Alternative character counting 77 B OPE structure constants 80 B.1 Equations from OPE bootstrap 80 B.2 Universal structure constants 82

show abstract

Super topological recursion and Gaiotto vectors for superconformal blocks

Osuga

2022

Lett Math Phys

View full text Add to dashboard Cite

For any (possibly singular) hyperelliptic curve, we give the definition of a hyperelliptic refined spectral curve and the hyperelliptic refined topological recursion, generalising the formulation for a special class of genus-zero curves by Kidwai and the author, and also improving the proposal by Chekhov and Eynard. Along the way, we uncover a fundamental geometric structure underlying the hyperelliptic refined topological recursion and investigate its properties -parts of which remain conjectural due to computational difficulties. Moreover, we establish a new recursion valid in the so-called Nekrasov-Shatashivili limit and prove existence of the corresponding quantum curve. Contents1. Introduction 2. Definitions 3. Properties 4. Q-top recursion and the Nekrasov-Shatashivili limit Appendix A.

show abstract

n-th parafermion $$ {\mathcal{W}}_N $$ characters from U(N) instanton counting on ℂ2/ℤn

Abstract: We propose, following the AGT correspondence, how the W para N,n (n-th parafermion W N) minimal model characters are obtained from the U(N) instanton counting on C 2 /Z n with Ω-deformation by imposing specific conditions which remove the minimal model null states.

Cited by 5 publications

References 65 publications

The Grassmannian VOA

The Grassmannian VOA

The Grassmannian VOA

Super topological recursion and Gaiotto vectors for superconformal blocks

Contact Info

Product

Resources

About