The 2-Dimensional Dual of $\phi^4$ in AdS$_3$

Abstract

We study the correlation functions of a conformally coupled $\phi^4$-interacting theory in AdS$_3$ and its dual CFT$_2$. The one-loop diagram is not expressible in terms of known transcendental functions, but is shown to be expressible as an infinite sum of previously well-studied tree-level diagrams, and we compute this sum using several number-theoretic conjectures. This enables us to extract recursively, the analytic expressions of anomalous dimensions of all dual double-trace operators. In the $s$-channel various consistency checks were performed against established bootstrap method, while our results in the $t$- and $u$-channel are not available in any previous literature to our knowledge.