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

Abstract

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 $Ad{S}_4\times {\mathbb{CP}}^3$ 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 $N/k^5$. Taking its flat space limit, we recover the known $R^4$ contribution to the type IIA S-matrix and reproduce the fact that it only receives perturbative contributions in $g_s$ from genus zero and genus one string worldsheets. This is the first check of AdS/CFT at finite $g_s$ for local operators. Our result for the four-point correlator interpolates between the large $N$, large 't Hooft coupling limit and the large $N$ finite $k$ limit. From the bulk perspective, this is an interpolation between type IIA string theory on $Ad{S}_4\times {\mathbb{CP}}^3$ at small string coupling and M-theory on $Ad{S}_4\times S^7/{\mathbb{Z}}_k$.

arXiv comment49 pages + Appendices,

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