## Abstract

Upon compactification on a circle, SU(N) gauge theory with all fields in the adjoint representation acquires a Z_{N} global symmetry because the center of the gauge group is Z_{N}. For N = 4 super Yang-Mills theory, we show how this Z^ topological symmetry arises in the context of the AdS/CFT correspondence, and why the symmetry group is Z_{N} rather than U(1). This provides a test of the AdS/CFT correspondence for finite N. If the theory is formulated on R^{3} x S^{1} with anti-periodic boundary conditions for fermions around the S^{1}, the topological symmetry is spontaneously broken; we show that the domain walls are D-strings, and hence that flux tubes associated with magnetic confinement can end on the domain walls associated with the topological symmetry. For the (0, 2) A_{N-1} sup er conformai field theory in six dimensions, we demonstrate an analogous phenomenon: a ZN global symmetry group arises if this theory is compactified on a Riemann surface. In this case, the domain walls are M-theory membranes.

Original language | English (US) |
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Pages (from-to) | XXVIII-13 |

Journal | Journal of High Energy Physics |

Volume | 2 |

Issue number | 11 |

DOIs | |

State | Published - 1998 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics

## Keywords

- Discrete and finite symmetries
- Field theories in higher dimensions
- Gauge symmetry
- Global symmetries