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

TL;DR

This paper uses the AdS$_3$/CFT$_2$ Virasoro-Shapiro amplitude to extract detailed strong-coupling data of the D1-D5 CFT, including scaling dimensions and three-point functions, advancing the understanding of AdS/CFT correspondence.

Contribution

It extends the Mellin formalism to the AdS$_3$/CFT$_2$ context, providing new analytic data for the D1-D5 CFT at strong coupling and translating Mellin data into R-symmetry spin basis.

Findings

Derived explicit formulas for scaling dimensions of long multiplets.

Computed three-point functions involving half-BPS operators.

Extended Mellin bootstrap to general KK configurations in AdS$_3$/CFT$_2$.

Abstract

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.