## Abstract

We study marginal and relevant supersymmetric deformations of the N=4 super Yang-Mills theory in four dimensions. Our primary innovation is the interpretation of the moduli spaces of vacua of these theories as non-commutative spaces. The construction of these spaces relies on the representation theory of the related quantum algebras, which are obtained from F-term constraints. These field theories are dual to superstring theories propagating on deformations of the AdS_{5}×S^{5} geometry. We study D-branes propagating in these vacua and introduce the appropriate notion of algebraic geometry for non-commutative spaces. The resulting moduli spaces of D-branes have several novel features. In particular, they may be interpreted as symmetric products of non-commutative spaces. We show how mirror symmetry between these deformed geometries and orbifold theories follows from T-duality. Many features of the dual closed string theory may be identified within the non-commutative algebra. In particular, we make progress towards understanding the K-theory necessary for backgrounds where the Neveu-Schwarz antisymmetric tensor of the string is turned on, and we shed light on some aspects of discrete anomalies based on the non-commutative geometry.

Original language | English (US) |
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Pages (from-to) | 196-248 |

Number of pages | 53 |

Journal | Nuclear Physics B |

Volume | 589 |

Issue number | 1-2 |

DOIs | |

State | Published - Nov 20 2000 |

## Keywords

- AdS/CFT
- D-branes
- K-theory
- Non-commutative geometry

## ASJC Scopus subject areas

- Nuclear and High Energy Physics