Gauge bosons and the AdS₃/LCFT₂ correspondence

We study the relationship between the gauge boson coupled to spin 2 operator and the singleton in three-dimensional anti-de Sitter space(AdS$_3$). The singleton can be expressed in terms of a pair of dipole ghost fields $A$ and $B$ which couple to $D$ and $C$ operators on the boundary of AdS$_3$. These operators form the logarithmic conformal field theory(LCFT$_2$). Using the correlation function for logarithmic pair, we calculate the greybody factor for the singleton. In the low temperature limit of $\omega \gg T_{\pm}$, this is compared with the result of the bulk AdS$_3$ calculation of the gauge boson. We find that the gauge boson cannot be realized as a model of the AdS$_3$/LCFT$_2$ correspondence.