Gauge fields and singletons of \(AdS_{2p+1}\) (Q1282056)

In this Letter we show that conformally invariant \(p\)-form field strengths, of conformal degree \(p\), and the associated \((p-1)\)-form potentials, in \(2p\)-dimensional Minkowski space, can be extended to a topological singleton field theory in \(AdS_{2p+1}\). The representations of \(\text{SO} (2p,2)\) carried by these fields are all zero-center modules, just as is the case for conformal electrodynamics in four dimensions (the case \(p=2)\). Fields of conformal degree \(p + 2\) describe massless fields in the bulk; they too are zero-center modules. In fact, these representations appear as part of the gauge sector in the singleton field module. Fields of this kind are known to be required by superconformal symmetry in the case \(p=2,3\); they may play a role for \(p=4,5\) as well, though simple super extensions of \(AdS_9\) and \(AdS_{11}\) do not exist. One may point out that the self-dual five form field strength of the \(10d\), \(IIB\) string is a `singleton' candidate for \(AdS_{11}\) in the sense of this paper. This may have some implications for attempts to construct a fundamental framework for strings or \(M\)-theory.