From weak to strong coupling in ABJM theory
type: Item
instance of: scholarly article
title: From weak to strong coupling in ABJM theory
zbMATH Open document ID: 1232.81043
author: Nadav Drukker
author: M. Mariño
author: Pavel Putrov
published in: Communications in Mathematical Physics
publication date: 2011-09-20T00:00:00Z
full work available at URL: https://arxiv.org/abs/1007.3837
full work available at URL: unige:17556
review text: The world-volume theory of coincident M2 branes discovered by \textit{O. Aharony, O. Bergman, D. L. Jafferis} and \textit{J. Maldacena} [J. High Energy Phys. 2008, No. 10, 091, 37 p. (2008; Zbl 1245.81130)] provides a new interacting field theory with well defined weak and strong coupling expansions. These two limits are \(\mathcal{N} = 6\) supersymmetric Chern-Simons matter on \({\mathbb{S}}^3\) and type IIA string theory on \(AdS_4 \times {\mathbb{CP}}^3\) (both descriptions are much more involved than their famous D3-brane analogs, 4d \(\mathcal{N} = 4\) supersymmetric Yang-Mills theory and type IIB string theory on \(Ad\,S_5\times\mathbb S^5\)). An important development was the reduction of the calculation of the partition function and certain Wilson loop observables in the gauge theory on \({\mathbb{S}}^3\) to finite dimensional integrals in a zero dimensional super-matrix model by \textit{A. Kapustin, B. Willett} and \textit{I. Yaakov} [``Exact results for Wilson loops in superconformal Chern-Simons theories with matter'', J. High Energy Phys. 2010, No. 10, 089, 21 p. (2010; \url{doi:10.1007/JHEP03(2010)089})]. The paper explores these recent observations further and extracts more exact results in ABJM theory from the matrix model, in particular the free energy which matches at strong coupling the classical supergravity action and gives the correct \(N^{3/2}\) scaling for the number of degrees of freedom of the M2 brane theory. Non-planar corrections are also calculated. The same matrix model appears also in the study of topological strings on a toric Calabi-Yau manifold, establishing a connection between the space of couplings of the planar ABJM theory and the moduli space of the latter. In particular it suggests that in addition to the usual perturbative and strong coupling (AdS) expansions a third 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 manifold and le…
reviewed by: Helmut Rumpf
Mathematics Subject Classification ID: 81T30
Mathematics Subject Classification ID: 83E30
Mathematics Subject Classification ID: 14J32
Mathematics Subject Classification ID: 58J28
Mathematics Subject Classification ID: 81T60
Mathematics Subject Classification ID: 83E50
zbMATH DE Number: 5948631
zbMATH Keywords: Chern-Simons theory
zbMATH Keywords: matrix models
zbMATH Keywords: weak-strong coupling duality
zbMATH Keywords: topological strings
zbMATH Keywords: Calabi-Yau manifolds
MaRDI profile type: Publication
OpenAlex ID: W3098357525
arXiv ID: 1007.3837
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DOI: 10.1007/S00220-011-1253-6
description: scientific article