The Aharony-Bergman-Jafferis-Maldacena theory on a circle

TL;DR

This work develops a bootstrap program for the celestial CFT dual to ABJM theory by exploiting 3D symmetries recast as 1D constraints on the celestial circle. It demonstrates that dual inversion can replace crossing symmetry in fixing the 4-point correlator, derives a fixed z dependent form z^{−1/6}(1−z)^{−1/6}, and computes conformal block expansion data including loop corrections starting at two loops. By analyzing the multi collinear limit, it extracts a leading two-particle OPE spectrum consistent with ABJM dynamics, revealing a two-particle operator in the X X̄ sector and indicating how spectrum information can be read from the multi-OPE. The results offer a general, symmetry driven framework for constructing CCFT data from higher dimensional theories and can be extended to higher point functions and other 3D/1D dual pairs.

Abstract

In this work, we bootstrap the 4-point correlators on the 1D celestial circle using 3D symmetries in the Aharony-Bergman-Jafferis-Maldacena theory as constraints. We find that the dual inversion property is strong enough to replace the crossing symmetry condition (or cyclic invariant condition) when bootstrapping. We also give some results about the conformal block expansion coefficients which contain the spectrum. Furthermore, we extract the OPE spectrum from the multi-collinear limit since all 3-point ABJM amplitudes vanish. Although we studied a specific theory, the methods used are valid for more general cases.