Free Energy of ABJM Theory

TL;DR

This paper computes the first non-vanishing quantum correction to the free energy of ABJM theory from the field theory perspective, revealing non-analytic behavior in the coupling and implications for the weak-strong coupling interpolation.

Contribution

It provides the first calculation of the 2-loop quantum correction to ABJM free energy, highlighting non-analyticity and the need for resummation due to infrared divergences.

Findings

The 2-loop correction is non-zero, unlike the 1-loop result.

Infrared divergences require resummation of ring diagrams.

The free energy likely interpolates smoothly between weak and strong coupling.

Abstract

The free energy of ABJM theory has previously been computed in the strong and weak coupling limits. In this note, we report on results for the computation of the first non-vanishing quantum correction to the free energy, from the field theory side. The correction can be expressed in terms of a thermal mass for the scalar fields. This mass vanishes to 1-loop order, but there is a non-vanishing result to 2-loop order. Hence, the leading correction to the free energy is non-analytic in the 't Hooft coupling constant lambda. The reason is that the infrared divergences necessitate a resummation of ring diagrams and a related reorganization of perturbation theory, in which already the leading correction receives contributions from all orders in lambda. These results suggest that the free energy interpolates smoothly between weak and strong coupling.