Description
We introduce a new supersymmetry index, dubbed the resolved elliptic
genus (REG), for the D1-D5 CFT on T^4. In a novel formulation of the
CFT at the symmetric orbifold point based on the Schur-Weyl duality, we
show how the REG can be naturally described and its protection is argued
based on a selection rule derived from the action of the deformed
supercharge. The REG is a one-parameter generalization of the standard
index, the modified elliptic genus (MEG), and gives more fine-grained
information about the structure of microstates than previously
available. We demonstrate precise matching of the REG between
supergravity and CFT below the black-hole threshold, where the MEG is
trivial. Above the threshold, we uncover a decomposition of black-hole
microstates into distinct sectors, invisible to the MEG. We expect both
the new formalism and the REG to provide useful tools for studying the
structure of black-hole microstates. In particular, we comment on their
possible relevance to the fortuity program for understanding black-hole
microstates within CFT.