### Abstract

The 4D self-dual Yang-Mills gauge theory on a self-dual space X is shown to be equivalent to a 2D sigma model valued in infinite dimensional gauge groups. Infinitesimal symmetries of the self-dual equation are obtained in terms of the sheaf cohomology group H
^{1} (T, script O signF(-2)), of the twistor space T corresponding to X. They are shown to form a symmetry algebra - a "CP
^{1}-extension" of the gauge symmetry algebra of a 2D sigma model which generalizes the Kac-Moody algebra as well as W
_{∞}.

Original language | English |
---|---|

Pages (from-to) | 105-110 |

Number of pages | 6 |

Journal | Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics |

Volume | 257 |

Issue number | 1-2 |

Publication status | Published - 1991 Dec 1 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

**Self-dual Yang-Mills (+gravity) as a 2D sigma model.** / Park, Q Han.

Research output: Contribution to journal › Article

*Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics*, vol. 257, no. 1-2, pp. 105-110.

}

TY - JOUR

T1 - Self-dual Yang-Mills (+gravity) as a 2D sigma model

AU - Park, Q Han

PY - 1991/12/1

Y1 - 1991/12/1

N2 - The 4D self-dual Yang-Mills gauge theory on a self-dual space X is shown to be equivalent to a 2D sigma model valued in infinite dimensional gauge groups. Infinitesimal symmetries of the self-dual equation are obtained in terms of the sheaf cohomology group H 1 (T, script O signF(-2)), of the twistor space T corresponding to X. They are shown to form a symmetry algebra - a "CP 1-extension" of the gauge symmetry algebra of a 2D sigma model which generalizes the Kac-Moody algebra as well as W ∞.

AB - The 4D self-dual Yang-Mills gauge theory on a self-dual space X is shown to be equivalent to a 2D sigma model valued in infinite dimensional gauge groups. Infinitesimal symmetries of the self-dual equation are obtained in terms of the sheaf cohomology group H 1 (T, script O signF(-2)), of the twistor space T corresponding to X. They are shown to form a symmetry algebra - a "CP 1-extension" of the gauge symmetry algebra of a 2D sigma model which generalizes the Kac-Moody algebra as well as W ∞.

UR - http://www.scopus.com/inward/record.url?scp=9344251489&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=9344251489&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:9344251489

VL - 257

SP - 105

EP - 110

JO - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

JF - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

SN - 0370-2693

IS - 1-2

ER -