BPS/CFT correspondence IV: sigma models and defects in gauge theory

Nikita Nekrasov

doi:10.1007/s11005-018-1115-7

BPS/CFT correspondence IV: sigma models and defects in gauge theory

Nikita Nekrasov

Simons Center for Geometry & Physics

Research output: Contribution to journal › Article › peer-review

58 Scopus citations

Abstract

Quantum field theory L ₁ on spacetime X ₁ can be coupled to another quantum field theory L ₂ on a spacetime X ₂ via the third quantum field theory L ₁₂ living on X ₁₂ = X ₁ ∩ X ₂ . We explore several such constructions with two- and four-dimensional X ₁ , X ₂ ’s and zero- and two-dimensional X ₁₂ ’s, in the context of N= 2 supersymmetry, non-perturbative Dyson–Schwinger equations, and BPS/CFT correspondence. The companion paper (Nekrasov, “BPS/CFT correspondence V: BPZ and KZ equations from qq-characters”, 2017. arXiv:1711.11582 [hep-th]) will show that the BPZ and KZ equations of two-dimensional conformal field theory are obeyed by the half-BPS surface defects in quiver N= 2 gauge theories.

Original language	English
Pages (from-to)	579-622
Number of pages	44
Journal	Letters in Mathematical Physics
Volume	109
Issue number	3
DOIs	https://doi.org/10.1007/s11005-018-1115-7
State	Published - Mar 4 2019

Keywords

BPS/CFT correspondence
Defects in quantum field theory
Hidden symmetry
Supersymmetry

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10.1007/s11005-018-1115-7

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title = "BPS/CFT correspondence IV: sigma models and defects in gauge theory",

abstract = " Quantum field theory L 1 on spacetime X 1 can be coupled to another quantum field theory L 2 on a spacetime X 2 via the third quantum field theory L 12 living on X 12 = X 1 ∩ X 2 . We explore several such constructions with two- and four-dimensional X 1 , X 2 {\textquoteright}s and zero- and two-dimensional X 12 {\textquoteright}s, in the context of N= 2 supersymmetry, non-perturbative Dyson{\textendash}Schwinger equations, and BPS/CFT correspondence. The companion paper (Nekrasov, {\textquotedblleft}BPS/CFT correspondence V: BPZ and KZ equations from qq-characters{\textquotedblright}, 2017. arXiv:1711.11582 [hep-th]) will show that the BPZ and KZ equations of two-dimensional conformal field theory are obeyed by the half-BPS surface defects in quiver N= 2 gauge theories.",

keywords = "BPS/CFT correspondence, Defects in quantum field theory, Hidden symmetry, Supersymmetry",

author = "Nikita Nekrasov",

note = "Publisher Copyright: {\textcopyright} 2018, Springer Nature B.V.",

year = "2019",

month = mar,

day = "4",

doi = "10.1007/s11005-018-1115-7",

language = "English",

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journal = "Letters in Mathematical Physics",

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TY - JOUR

T1 - BPS/CFT correspondence IV

T2 - sigma models and defects in gauge theory

AU - Nekrasov, Nikita

PY - 2019/3/4

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N2 - Quantum field theory L 1 on spacetime X 1 can be coupled to another quantum field theory L 2 on a spacetime X 2 via the third quantum field theory L 12 living on X 12 = X 1 ∩ X 2 . We explore several such constructions with two- and four-dimensional X 1 , X 2 ’s and zero- and two-dimensional X 12 ’s, in the context of N= 2 supersymmetry, non-perturbative Dyson–Schwinger equations, and BPS/CFT correspondence. The companion paper (Nekrasov, “BPS/CFT correspondence V: BPZ and KZ equations from qq-characters”, 2017. arXiv:1711.11582 [hep-th]) will show that the BPZ and KZ equations of two-dimensional conformal field theory are obeyed by the half-BPS surface defects in quiver N= 2 gauge theories.

AB - Quantum field theory L 1 on spacetime X 1 can be coupled to another quantum field theory L 2 on a spacetime X 2 via the third quantum field theory L 12 living on X 12 = X 1 ∩ X 2 . We explore several such constructions with two- and four-dimensional X 1 , X 2 ’s and zero- and two-dimensional X 12 ’s, in the context of N= 2 supersymmetry, non-perturbative Dyson–Schwinger equations, and BPS/CFT correspondence. The companion paper (Nekrasov, “BPS/CFT correspondence V: BPZ and KZ equations from qq-characters”, 2017. arXiv:1711.11582 [hep-th]) will show that the BPZ and KZ equations of two-dimensional conformal field theory are obeyed by the half-BPS surface defects in quiver N= 2 gauge theories.

KW - BPS/CFT correspondence

KW - Defects in quantum field theory

KW - Hidden symmetry

KW - Supersymmetry

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DO - 10.1007/s11005-018-1115-7

M3 - Article

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SP - 579

EP - 622

JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

IS - 3

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BPS/CFT correspondence IV: sigma models and defects in gauge theory

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