## 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 |
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Pages (from-to) | 579-622 |

Number of pages | 44 |

Journal | Letters in Mathematical Physics |

Volume | 109 |

Issue number | 3 |

DOIs | |

Publication status | Published - 4 Mar 2019 |

Externally published | Yes |

## Keywords

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