Coherent (spin-)tensor fields on D = 4 anti-de Sitter space

Abstract

The coherent states associated to the discrete series representations D(E o , s) of SO(3, 2) are constructed in terms of (spin-)tensor fields on D = 4 anti-de Sitter space. For E o > s + 5 the linear space H Eo,s spanned by these states is proved to carry the unitary irreducible representation D(E o , s). The SO(3, 2)-covariant generalized Fourier transform in this space is exhibited. The quasiclassical properties of the coherent states are analyzed. In particular, these states are shown to be localized on the time-like geodesics of anti-de Sitter space.

On singleton composites in non-compact WZW models

“…In order to demonstrate how the spectral flow operation acts in the free field basis, let us begin by looking more closely at the twist fields Σ , which realize P -twisted primary fields in the sense of (3.21) and (3.22), obey conditions that are stronger than those in (5.64). We next expand the twist fields in modes, |0 , (5.67) 18 There also exist other massive fields in the model with higher conformal weights which will not be considered here. The maximal conformal weight for a given spin m is given by h ′…”

“…The model nonetheless contains non-unitary and non-topological states. Drawing on the continuum limit of discretized branes [15] as well as on the sigmamodel description of null surfaces in anti-de Sitter spacetime [17] (see also [18,19]), it makes sense to entertain the idea that the coset model based on…”

“…where we have suppressed the cocycle factor. These fields obey |0 , (5.67) 18 There also exist other massive fields in the model with higher conformal weights which will not be considered here. The maximal conformal weight for a given spin m is given by h ′…”