Nonperturbative aspects of ABJM theory (1103.4844v2)

Abstract: Using the matrix model which calculates the exact free energy of ABJM theory on S^3 we study non-perturbative effects in the large N expansion of this model, i.e., in the genus expansion of type IIA string theory on AdS4xCP^3. We propose a general prescription to extract spacetime instanton actions from general matrix models, in terms of period integrals of the spectral curve, and we use it to determine them explicitly in the ABJM matrix model, as exact functions of the 't Hooft coupling. We confirm numerically that these instantons control the asymptotic growth of the genus expansion. Furthermore, we find that the dominant instanton action at strong coupling determined in this way exactly matches the action of an Euclidean D2-brane instanton wrapping RP^3.

• The paper introduces a matrix model method to extract instanton actions as periods of the spectral curve in ABJM theory.
• It verifies numerically that the instanton actions dictate the genus expansion rate and correspond to D2-brane configurations.
• It suggests that Borel summability in the strong coupling regime underpins a nonperturbative completion of the partition function.

Nonperturbative Aspects of ABJM Theory: An Expert Overview

The paper, "Nonperturbative Aspects of ABJM Theory," authored by Nadav Drukker, Marcos Mariño, and Pavel Putrov, investigates the nonperturbative physics inherent in the ABJM (Aharony-Bergman-Jafferis-Maldacena) theory. Employing a matrix model approach, it systematically analyzes the large $N$ expansion of ABJM theory, specifically in the strong coupling regime, which corresponds to the IIA string theory on AdS$_4 \times \mathbb{CP}^3$. The research explores deriving spacetime instanton actions as functions of the 't Hooft coupling, using period integrals of the spectral curve associated with the matrix model.

Key Contributions

• Instanton Actions: The authors propose a novel method to extract spacetime instanton actions from matrix models, identifying them as periods of the spectral curve. These instanton actions elucidate the nonperturbative landscape that governs the critical properties and asymptotic behaviors associated with the ABJM matrix model at large orders.
• Genus Expansion and Numerical Verification: The research provides compelling numerical evidence to confirm that the calculated instanton actions indeed dictate the growth rate of the genus expansion. Notably, the dominant instanton action at strong coupling aligns with the action of an Euclidean D2-brane instanton wrapping a 3-cycle in the internal space $\mathbb{CP}^3$.
• Universal Structure of Instantons: The paper asserts the hypothesis that instanton actions can be expressed as complex linear combinations of periods specific to the moduli space governed by special geometry. This hypothesis extends analogous results from non-critical string theory to the field of ABJM theory.

Implications and Speculations

• Borel Summability: One intriguing observation is that in regions of strong coupling, the genus expansion seems Borel summable, implying that it enables a stable perturbation series that can be resummed to ascertain complete information about the partition function. This property highlights a potential method to tackle the nonperturbative completion of the theory.
• Gauge/String Duality Insights: The work provides crucial insights into the AdS/CFT correspondence through the lens of large $N$ limits and nonperturbative effects, offering a precise characterization of dual string theories via a complete gauge theory description.
• Future Scope in Quantum Gravity: The identification of instantons with D-brane configurations could inspire further studies in backgrounds of quantum gravity and string theory, advancing our understanding of M-theory compactifications, the role of D-branes in singularity resolutions, and their implication on cosmological models.

The paper not only contributes significantly to the theoretical understanding of ABJM theory by linking matrix model computations with geometric interpretations in string theory but also sets a foundation for future explorations of nonperturbative phenomena in other gauge theories with known string duals. The tools and methodologies developed here are likely to find applications in broader studies of holography and dual conformal field theories, potentially uncovering new domains of string theory.