BPS Chaos in the D1-D5 CFT

We explore the emergence of chaotic dynamics within the protected BPS sectors of the D1-D5-P system, with a particular focus on the fate of states with nonzero right-moving R-charge $j_R$. While the elliptic genus captures an index of BPS states immune to lifting under deformations, the full BPS partition function—refined by $j_L$ and $j_R$—provides a more granular view of the spectrum and its potential sensitivity to moduli. We investigate whether states with $j_R \neq 0$, associated with black hole "hair," survive deformations away from the orbifold point, and whether their degeneracies can grow parametrically to account for black hole entropy.