From weak to strong coupling in ABJM theory

TL;DR

This paper analyzes the ABJM theory's matrix model, deriving exact results for free energy and Wilson loops, confirming strong coupling predictions, and exploring connections to topological strings and Calabi-Yau geometries.

Contribution

It provides new exact calculations of free energy and Wilson loops in ABJM theory, including non-planar corrections and instanton effects, and uncovers a novel expansion related to Calabi-Yau moduli.

Findings

Planar free energy matches supergravity at strong coupling.

Identifies world-sheet instanton contributions in CP^3.

Discovers a new expansion locus related to Calabi-Yau conifold point.

Abstract

The partition function of N=6 supersymmetric Chern-Simons-matter theory (known as ABJM theory) on S^3, as well as certain Wilson loop observables, are captured by a zero dimensional super-matrix model. This super-matrix model is closely related to a matrix model describing topological Chern-Simons theory on a lens space. We explore further these recent observations and extract more exact results in ABJM theory from the matrix model. In particular we calculate the planar free energy, which matches at strong coupling the classical IIA supergravity action on AdS_4 x CP^3 and gives the correct N^{3/2} scaling for the number of degrees of freedom of the M2 brane theory. Furthermore we find contributions coming from world-sheet instanton corrections in CP^3. We also calculate non-planar corrections, both to the free energy and to the Wilson loop expectation values. This matrix model appears also in the study of topological strings on a toric Calabi-Yau manifold, and an intriguing connection arises between the space of couplings of the planar ABJM theory and the moduli space of this Calabi-Yau. In particular it suggests that, in addition to the usual perturbative and strong coupling (AdS) expansions, a third natural expansion locus is the line where one of the two 't Hooft couplings vanishes and the other is finite. This is the conifold locus of the Calabi-Yau, and leads to an expansion around topological Chern-Simons theory. We present some explicit results for the partition function and Wilson loop observables around this locus.