### Abstract

For a quiver with weighted arrows, we define gauge-theory K-theoretic W-algebra generalizing the definition of Shiraishi et al. and Frenkel and Reshetikhin. In particular, we show that the qq-character construction of gauge theory presented by Nekrasov is isomorphic to the definition of the W-algebra in the operator formalism as a commutant of screening charges in the free field representation. Besides, we allow arbitrary quiver and expect interesting applications to representation theory of generalized Borcherds–Kac–Moody Lie algebras, their quantum affinizations and associated W-algebras.

Original language | English |
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Pages (from-to) | 1-31 |

Number of pages | 31 |

Journal | Letters in Mathematical Physics |

DOIs | |

Publication status | Accepted/In press - 2018 Mar 21 |

### Fingerprint

### Keywords

- Conformal field theories
- instanton
- Quantum groups
- Quiver
- Supersymmetric gauge theories
- W-algebras

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Letters in Mathematical Physics*, 1-31. https://doi.org/10.1007/s11005-018-1072-1

**Quiver W-algebras.** / Kimura, Taro; Pestun, Vasily.

Research output: Contribution to journal › Article

*Letters in Mathematical Physics*, pp. 1-31. https://doi.org/10.1007/s11005-018-1072-1

}

TY - JOUR

T1 - Quiver W-algebras

AU - Kimura, Taro

AU - Pestun, Vasily

PY - 2018/3/21

Y1 - 2018/3/21

N2 - For a quiver with weighted arrows, we define gauge-theory K-theoretic W-algebra generalizing the definition of Shiraishi et al. and Frenkel and Reshetikhin. In particular, we show that the qq-character construction of gauge theory presented by Nekrasov is isomorphic to the definition of the W-algebra in the operator formalism as a commutant of screening charges in the free field representation. Besides, we allow arbitrary quiver and expect interesting applications to representation theory of generalized Borcherds–Kac–Moody Lie algebras, their quantum affinizations and associated W-algebras.

AB - For a quiver with weighted arrows, we define gauge-theory K-theoretic W-algebra generalizing the definition of Shiraishi et al. and Frenkel and Reshetikhin. In particular, we show that the qq-character construction of gauge theory presented by Nekrasov is isomorphic to the definition of the W-algebra in the operator formalism as a commutant of screening charges in the free field representation. Besides, we allow arbitrary quiver and expect interesting applications to representation theory of generalized Borcherds–Kac–Moody Lie algebras, their quantum affinizations and associated W-algebras.

KW - Conformal field theories

KW - instanton

KW - Quantum groups

KW - Quiver

KW - Supersymmetric gauge theories

KW - W-algebras

UR - http://www.scopus.com/inward/record.url?scp=85044242087&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85044242087&partnerID=8YFLogxK

U2 - 10.1007/s11005-018-1072-1

DO - 10.1007/s11005-018-1072-1

M3 - Article

AN - SCOPUS:85044242087

SP - 1

EP - 31

JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

SN - 0377-9017

ER -