Near horizon limits of massless BTZ and their CFT duals

We consider the massless 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 spacelike singular AdS3/Z_K orbifold in the large K limit, the "pinching orbifold". We show that from the dual 2d CFT viewpoint, the null orbifold corresponds to the p^+=0 sector of the Discrete Light-Cone Quantisation (DLCQ) 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 in both the right and left sectors of the 2d CFT, essentially leaving us with the states L_0=\bar L_0=c/24 only. In the latter case, one can combine the near horizon limit with sending the 3d Planck length l_P to zero, or equivalently the dual CFT central charge c to infinity. We provide preliminary evidence that in that case some nontrivial dynamics may survive the limit.