%0 Journal Article
%T Anti-de Sitter Space and the Center of the Gauge Group
%A Ofer Aharony
%A Edward Witten
%J Physics
%D 1998
%I arXiv
%R 10.1088/1126-6708/1998/11/018
%X 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 $Z_N$ "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 $R^3 \times S^1$ 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) $A_{N-1}$ superconformal field theory in six dimensions, we demonstrate an analogous phenomenon: a $Z_N$ global symmetry group arises if this theory is compactified on a Riemann surface. In this case, the domain walls are M-theory membranes.
%U http://arxiv.org/abs/hep-th/9807205v1