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We revisit the holographic dictionary for a free massless scalar in AdS$_3$,focusing on the `singleton' solutions for which the boundary profile is anarbitrary chiral function. We look for consistent boundary conditions whichinclude this class of solutions. On one hand, we give a no-go argument thatthey cannot be interpreted within any boundary condition which preserves fullconformal invariance. On the other hand, we show that such solutions fitnaturally in a generalization of the Comp\`{e}re-Song-Strominger boundaryconditions, which preserve a chiral Virasoro and current algebra. Theseobservations have implications for the black hole deconstruction proposal,which proposes singleton solutions as candidate black hole microstategeometries. Our results suggest that the chiral boundary condition, which alsocontains the extremal BTZ black hole, is the natural setting forholographically interpreting the black hole deconstruction proposal.

Chiral boundary conditions for singletons and W-branes