From Weak to Strong Coupling in ABJM Theory

By N. Drukker, Marcos Mariño, Pavel Putrov. 2010

640 citations recorded by the source corpus.

The partition function of $${\mathcal{N}=6}$$ supersymmetric Chern–Simons-matter theory (known as ABJM theory) on $${\mathbb{S}^3}$$ , 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 $${{\rm AdS}_4\times\mathbb{C}\mathbb{P}^3}$$ and gives the correct N3/2 scaling for the number of degrees of freedom of the M2 brane theory. Furthermore we find contributions coming from world-sheet instanton corrections in $${\mathbb{C}\mathbb{P}^3}$$ . 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.

Subfields: Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/3d1aea891181a49fae5bba68e357c239b5f4f9b7

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Citations in the corpus

Numerical studies of the ABJM theory for arbitrary N at arbitrary coupling constant (2012, methodology): “The leading largeN behavior of the plotted quantity is π√ 2 ( 124 + 1 3k2 )k3/2 √ N for FHM and π 24 √ 2 k3/2 √ N for DMP, where the difference comes from the λ2/(3N2) = 1/(3k2) term in (2.9).”
Towards the F-theorem: $ \mathcal{N} = 2 $ field theories on the three-sphere (2011, positive): “matrix integrals for theories with known M-theory duals [9,10,15] produce perfect agreement with (1.”
Chern–Simons theory with vector fermion matter (2011, methodology): “It has recently been realized that the partition functions of supersymmetric ChernSimons theories on S are often exactly computable via the techniques of supersymmetric localization [54–57].”
The exact superconformal R-symmetry extremizes Z (2010, methodology): “This method has been put to impressive use by Drukker, Marino, and Putrov [11] (see also [18, 30]), who found the famous N scaling of the entropy of multiple M2 branes directly in the IR N = 6 conformal field”
Duality Symmetric String and M-Theory (2013, methodology): “The signature N3/2 degree of freedom scaling has been rigorously demonstrated for these Chern-Simons matter type theories [224].”
Fivebranes and 3-manifold homology (2016, background): “In the case M3 = L(2, 1) the explicit form of such transform was found in [104, 105]”
4d Index to 3d Index and 2d TQFT (2011, background): “Recent studies have uncovered powerful techniques (mostly based on localization) to extract exact results for 3d and 4d supersymmetric gauge theories, including the 4d N ≥ 1 superconformal index on S(1) × S(3) [1, 2], the 4d N ≥ 2 partition function on S(4) [3], the 3d N ≥ 2 partition function on S(”
Relation between the 4d superconformal index and the S3 partition function (2011, methodology): “It is used to confirm dualities among 3d theories [4, 5, 6, 7] and predictions of AdS4/CFT3 [8, 9, 10, 11, 12].”
The gravity dual of supersymmetric gauge theories on a squashed three-sphere (2011, methodology): “In [27] the free energy of the ABJM matrix model arising from localization on the round three-sphere was matched to the dual holographic free energy in the large N limit, in particular reproducing the famous N gravity prediction from a purely field theoretic computation.”
M5-branes from gauge theories on the 5-sphere (2012, background): “Although the N3/2 scalings for N coincident M2-branes have been recently understood in some detail [4, 5], the N3 scalings for N M5-branes are not very solidly understood in a microscopic way.”
Refined stable pair invariants for E-, M- and [p, q]-strings (2013, background): “The topological string on the del Pezzo surfaces captures [15] the topological sector [16] of three-dimensional ABJM theories proposed for the description of multiple M2-branes[17] even at strong coupling and recently it was found that the 1 = 0 sector of the refined topological string encodes the n”
Multimatrix models and tri-Sasaki Einstein spaces (2010, methodology): “Remarkably, this surprising prediction was recently confirmed [5] in the context of the ABJM construction [6] of the U(N)k×U(N)−k Chern-Simons gauge theory on coincident M2-branes.”
Non-perturbative effects and the refined topological string (2013, methodology): “As we mentioned in the introduction, the results of [6, 20] indicate that the ABJM matrix model derived in [5] provides a non-perturbative definition of topological string theory on local P1 × P1.”
Index for three dimensional superconformal field theories with general R-charge assignments (2011, methodology): “The surprising prediction of AdS4/CFT3 duality, the N 3/2 scaling[2] of the partition function, was recently confirmed on the CFT side for theories with N ≥ 3 supersymmetry[3, 4].”
The large N limit of quiver matrix models and Sasaki-Einstein manifolds (2011, methodology): “Finally, it would be interesting to apply the matrix model techniques of [5, 8] to the theories studied in this paper.”
Instanton effects in ABJM theory from Fermi gas approach (2012, methodology): “There is much progress in this matrix model including the derivation of the degree of freedom N [6] expected from the AdS/CFT correspondence [7] and its perturbative completion by the Airy function [8].”