STRESS-TENSOR COMMUTATORS AND SCHWINGER TERMS IN SINGLETON THEORIES

We compute the commutators of the regularized quantum stress-tensor of singleton theories formulated on the boundary of a (p+2)-dimensional anti de Sitter space (AdS_p+2). (These are superconformal field theories on S^p×S¹.) We find that the commutator algebra contains the finite dimensional AdS_p+2 algebra SO(p+1, 2). We also find field dependent as well as field independent Schwinger terms (i.e. central extensions), which, however, do not lead to anomalies in the algebra of the AdS charges. We also give a simple derivation of the two-point functions for bosonic and fermionic singletons.