From weak to strong coupling in ABJM theory (1007.3837v4)

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.

• The paper introduces a zero-dimensional super-matrix model that captures the partition function of ABJM theory on S³.
• It computes the planar free energy matching type IIA supergravity predictions and confirms the N^(3/2) scaling for M2-brane dynamics.
• It identifies worldsheet instanton and non-planar corrections that provide deeper insight into non-perturbative effects and duality in Chern-Simons matter theories.

From Weak to Strong Coupling in ABJM Theory: An Expert Overview

The research paper titled "From weak to strong coupling in ABJM theory" by Nadav Drukker, Marcos Mariño, and Pavel Putrov, presents a meticulous examination of the Aharony-Bergman-Jafferis-Maldacena (ABJM) theory, mapping out its characteristics from weak to strong coupling regimes. This paper provides a rich understanding of the duality between three-dimensional Chern-Simons matter theories and type IIA string theory, contributing siginficantly to the understanding of M2-brane dynamics.

Key Findings and Results

1. Matrix Model Description: A key contribution of the paper is the formulation of a zero-dimensional super-matrix model that captures the partition function of the $\mathcal{N}=6$ supersymmetric Chern-Simons-matter theory on $S^3$. This model parallels the matrix model for topological Chern-Simons theory on a lens space, providing a powerful tool to extract exact results in ABJM theory.
2. Planar Free Energy and Strong Coupling Matching: The authors calculate the planar free energy, showing strong coupling concordance with the classical type IIA supergravity action on $AdS_4 \times \mathbb{CP}^3$. This establishes the correct $N^{3/2}$ scaling law for the M2-brane theory degrees of freedom, offering a solid agreement with predictions from M-theory perspectives.
3. Worldsheet Instanton Contributions: The research identifies contributions from world-sheet instanton corrections within the $\mathbb{CP}^3$ space, delivering key insights into non-perturbative effects which manifest at specific scaling orders in the coupling constant.
4. Non-Planar Corrections: Extending their analysis, the authors calculate non-planar corrections both on the free energy and Wilson loop expectation values. These findings offer a glimpse into the intricate behavior of such observables beyond the planar limit, enhancing the understanding of $1/N$ expansions in super-Chern-Simons theories.
5. Moduli Space and Duality Frames: By exploring the moduli space of the theory, intriguing connections are drawn between ABJM theory's coupling space and the moduli space of toric Calabi-Yau manifolds. The paper suggests alternative expansion loci, including the conifold locus, a third natural expansion site aligning with topological Chern-Simons theory.
6. Interplay with Topological Strings: The paper posits a fascinating connection between ABJM matrix models and topological string theory on toric Calabi-Yau manifolds, framing the emergence of instanton corrections and elucidating the rich geometric structure underlying the field-theory dual.

Implications and Future Research

The implications of these findings traverse both theoretical formulations and practical computations in supersymmetric gauge theories. The application of matrix models to uncover exact results strengthens dualities across different dimensions and fosters more precise predictions from holographic principle standpoints. Furthermore, this work lays groundwork for future explorations into higher-loop corrections and non-perturbative expansions, offering pathways to unify various dual descriptions of M-theory and quantum gravity scenarios.

In summary, this paper underscores the efficacy of matrix models in elucidating the structural properties of complex quantum field theories and stimulates further investigation into the duality frameworks that underlie modern theoretical physics. As the paper aligns with and extends existing string theory conjectures, it remains pivotal for researchers seeking deeper insights into gauge/gravity dualities and the landscape of high-energy theoretical physics.