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

TL;DR

This paper analyzes half-BPS operators in N=4 super Yang-Mills with SU(N) gauge group at finite N, providing exact formulas, dual bases, and extending previous results from U(N) to SU(N).

Contribution

It introduces an exact formula for null basis operators, establishes their duality with multi-trace operators, and constructs a diagonal basis using higher Hamiltonians.

Findings

Exact formula for null basis operators in SU(N)

Duality between null basis and multi-trace basis

Extension of factorization and probability results to SU(N)

Abstract

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.