Gauge bosons and the AdS_3/LCFT_2 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.