AdS$_4$/CFT$_3$ from Weak to Strong String Coupling

Understand

We consider the four-point function of operators in the stress tensor multiplet of the $U(N)_k\times U(N)_{-k}$ ABJM theory, in the limit where $N$ is taken to infinity while $N/k^{5}$ is held fixed.

• In this limit, ABJM theory is holographically dual to type IIA string theory on $AdS_4\times \mathbb{CP}^3$ at finite string coupling $g_s \sim (N/k^5)^{1/4}$.
• While at leading order in $1/N$, the stress tensor multiplet four-point function can be computed from type IIA supergravity, in this work we focus on the first subleading correction, which comes from tree level Witten diagrams with an $R^4$ interaction vertex.
• Using superconformal Ward identities, bulk locality, and the mass deformed sphere free energy previously computed to all orders in $1/N$ from supersymmetric localization, we determine this $R^4$ correction as a function of $N/k^5$.