The Fate of 1/4-BPS States in the D1-D5 CFT

Abstract

We consider the 1/4-BPS operators in the D1-D5 system on AdS$_3\times S^3\times T^4$. We evaluate the anomalous dimensions of low-lying sectors in conformal perturbation theory around Sym$^N(T^4)$ exactly in $N$. All anomalous dimensions are consistent with recombination of the short multiplets into long ones and take a particularly simple form. We show that at finite $N$ and at first nontrivial order in the deformation, for the sectors we consider, the BPS density of states agrees with that of the supergravity point. To the order in conformal perturbation theory we consider, this confirms that not all states that can get lifted do get lifted.