D1-D5 CFT data from AdS3 × S3 Virasoro-Shapiro amplitude

A bstract The AdS Virasoro-Shapiro amplitude has recently been generalized to the AdS 3 /CFT 2 correspondence between type IIB string theory on AdS 3 × S 3 × K 3 (or T 4 ), supported by Ramond-Ramond flux, and the D1-D5 CFT. In this paper, we use the AdS × 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 opera-tors with arbitrary external KK modes, we employ the full AdS × S Mellin formalism to bootstrap the AdS 3 × 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 × SU(2) R R-symmetry spins. As applications, we obtain explicit formulae for the scaling dimensions of long multiplets on the first two even-spin 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.