2 00 8 QMUL - PH - 07 - 08 Half - BPS SU ( N ) Correlators in N = 4 SYM T . W . Brown ⋆ Centre for Research in String Theory Department of Physics Queen

In this note we study half-BPS operators in N = 4 super Yang-Mills for gauge group SU(N) at finite N. In particular we elaborate on the results of hep-th/0410236, providing an exact formula for the null basis operators algorithmically constructed there. For gauge groups U(N) and SU(N) we show that this basis is dual to the basis of multi-trace operators with respect to the two point function. We use this to extend the results of hep-th/0611290 concerning factorisation and probabilities from U(N) to SU(N). We also give a construction for a separate diagonal basis of the SU(N) operators in terms of the higher Hamiltonians of the complex matrix model reduction of this sector.