Mellin transforming the minimal model CFTs: AdS/CFT at strong curvature

TL;DR

The paper investigates whether two-dimensional minimal model CFTs admit a string-dual description by applying the Mellin transform to their 4-point functions. By expressing these correlators as sums of conformal blocks and mapping their Mellin transforms to Koba-Nielsen open-string amplitudes, the authors uncover meromorphic Mellin amplitudes with Regge-like pole towers and polynomial residues, interpreted as boundary S-matrix data for a bulk theory in $AdS_3$ with string-scale curvature. The explicit Ising-model example confirms the universal pole structure and infinite towers of massive states, supporting a dual open-string interpretation without a conventional low-energy gravity limit. Overall, the work provides concrete evidence for Mack’s conjecture in a 2D setting and suggests a local bulk description in $AdS_3$ governed by a meromorphic Mellin framework rather than a perturbative genus expansion.

Abstract

Mack has conjectured that all conformal field theories are equivalent to string theories. We explore the example of the two-dimensional minimal model CFTs and confirm that the Mellin transformed amplitudes have the desired properties of string theory in three-dimensional anti-de Sitter spacetime.