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

TL;DR

This paper analyzes correlation functions in a $ ext{AdS}_3$ $ ext{CFT}_2$ duality for a $ ext{phi}^4$ theory, deriving anomalous dimensions of double-trace operators through novel summation techniques and consistency checks.

Contribution

It introduces a new method to compute one-loop diagrams in AdS$_3$/CFT$_2$ and derives analytic expressions for anomalous dimensions of dual operators, including previously unavailable channels.

Findings

Expressed one-loop diagrams as sums of tree-level diagrams using number theory.

Computed anomalous dimensions of all dual double-trace operators recursively.

Performed consistency checks in the s-channel against bootstrap methods.

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.