Half-BPS SU (N) correlators in 𝒩= 4 SYM

摘要: In this note we study half-BPS operators in Script 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.