D1-D5 CFT data from $AdS_3 \times S^3$ Virasoro-Shapiro amplitude

The AdS Virasoro-Shapiro amplitude has recently been generalized to the AdS$_3$/CFT$_2$ correspondence between type IIB string theory on $AdS_3 \times S^3 \times K3$ (or $T^4$), supported by Ramond-Ramond flux, and the D1-D5 CFT. In this paper, we use the $AdS\times S$ Virasoro-Shapiro machinery to extract strong-coupling CFT data of the D1-D5 CFT by extending and completing earlier analyses in several directions. First, starting from the superconformal/Mellin block expansion of four-point functions of half-BPS tensor operators with arbitrary external KK modes, we employ the full $AdS\times S$ Mellin formalism to bootstrap the $AdS_3 \times S^3$ Virasoro-Shapiro amplitude for general KK configurations. This establishes its consistency with superconformal symmetry and yields a wealth of additional CFT data naturally organized in internal Mellin space. Second, we push the computation to the next order in the strong-coupling expansion and extract additional higher-order CFT data. Third, we translate the resulting Mellin-space data into the internal spin basis. We derive the transformation kernel relating internal Mellin variables and $SU(2)_L \times SU(2)_R$ R-symmetry spins. As applications, we obtain explicit formulae for the scaling dimensions of long multiplets on the first two leading Regge trajectories of arbitrary internal spins, and certain three-point functions with half-BPS tensor operators. These results provide a valuable set of analytic D1-D5 CFT data, enabling future applications and direct comparison with complementary approaches such as integrability.