Near-horizon limits of massless BTZ and their CFT duals

We consider the massless Banados-Teitelboim-Zanelli (BTZ) black hole and show that it is possible to take its 'near-horizon' limit in two distinct ways. The first one leads to a null self-dual orbifold of AdS3 and the second to a singular spacelike AdS3/ZK orbifold in the large K limit, the 'pinching orbifold'. We show that from the dual 2D conformal field theory (CFT) viewpoint, the null orbifold corresponds to the p+ = 0 sector of the discrete light-cone quantization of the 2D CFT where a chiral sector of the CFT is decoupled, while the pinching orbifold corresponds to taking an infinite mass gap limit on both the right and left sectors of the 2D CFT, essentially leaving us with the states L0=L-bar0= c/24 only. In the latter case, one can combine the near-horizon limit with sending the 3D Planck length lP to zero or equivalently the dual 2D CFT central charge c to infinity. We provide preliminary evidence that in the latter case some nontrivial dynamics may survive the limit.