Exact results in ABJM theory from topological strings

By Marcos Mariño, Pavel Putrov. 2009

314 citations recorded by the source corpus.

Recently, Kapustin, Willett and Yaakov have found, by using localization techniques, that vacuum expectation values of Wilson loops in ABJM theory can be calculated with a matrix model. We show that this matrix model is closely related to Chern-Simons theory on a lens space with a gauge supergroup. This theory has a topological string large N dual, and this makes possible to solve the matrix model exactly in the large N expansion. In particular, we find the exact expression for the vacuum expectation value of a 1/6 BPS Wilson loop in the ABJM theory, as a function of the 't Hooft parameters, and in the planar limit. This expression gives an exact interpolating function between the weak and the strong coupling regimes. The behavior at strong coupling is in precise agreement with the prediction of the AdS string dual. We also give explicit results for the 1/2 BPS Wilson loop recently constructed by Drukker and Trancanelli.

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

View Paper: https://www.semanticscholar.org/paper/c6db90bef8ead7ab1e7795f62fa8e30b2ca86a6e

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Citations in the corpus

Instanton effects in ABJM theory from Fermi gas approach (2012, background): “1 Topological String on Local F0 As discussed in [20, 6], the ABJM matrix model (2.”
Numerical studies of the ABJM theory for arbitrary N at arbitrary coupling constant (2012, methodology): “2 By using this matrix model, the free energy of the ABJM theory has been studied intensively [28, 29, 30, 31, 32, 33, 34, 35].”
ABJM theory as a Fermi gas (2011, methodology): “In the context of ABJM theory, as explained in detail in [26, 5], the relevant quantities correspond to topological string computations in the so-called orbifold frame, where the natural periods are λ (the ’t Hooft coupling of the gauge theory) and the derivative ∂λF0.”
Notes on SUSY gauge theories on three-sphere (2010, methodology): “It has also been applied to the study of the ABJM theory at strong coupling, in particular its conjectured O(N3/2) growth of the degrees of freedom[10, 11, 12].”
Exact results for the entanglement entropy and the energy radiated by a quark (2013, methodology): “The weak coupling expansion can be easily done (in the planar limit) using the matrix model of [15, 53]”
From Weak to Strong Coupling in ABJM Theory (2010, methodology): “30) can be written in closed form [8], like the integrals (2.”
Summing up all genus free energy of ABJM matrix model (2011, methodology): “The ABJM matrix model is equivalent to the so-called Lens space matrix model [23, 24], which computes the partition function of the U(N1) × U(N2) branch of the Chern-Simons theory on the Lens space L(2, 1) = S(3)/Z2, by the analytic continuation N2 → −N2 [22].”
The large N limit of quiver matrix models and Sasaki-Einstein manifolds (2011, methodology): “In particular, the matrix model for the ABJM theory was solved in [34, 5] in the limit in which N is large and k/N is held fixed.”
Lectures on non‐perturbative effects in large N gauge theories, matrix models and strings (2012, background): “16) the spectral curve is given by the equation [2, 74, 99, 51]”
Multimatrix models and tri-Sasaki Einstein spaces (2010, methodology): “This matrix model was solved in the large N limit with N/k kept fixed [5, 9], leading to precise tests of the AdS/CFT correspondence for Wilson loops and for the free energy (by which we mean minus the logarithm of the Euclidean partition function).”
Non-perturbative effects and the refined topological string (2013, background): “This is certainly natural from the point of view of the duality between this topological string and ChernSimons theory on RP3 [22], and the relation between the Chern-Simons matrix model on RP3 and the ABJM matrix model [20].”
Lectures on localization and matrix models in supersymmetric Chern–Simons-matter theories (2011, methodology): “To do this, we present the localization technique of [61] and the matrix model techniques of [47, 75, 32].”
Topological Strings from Quantum Mechanics (2014, background): “The study of the ABJM matrix model indicated a close connection to topological string theory: its ’t Hooft expansion is identical to the genus expansion of the topological string on the Calabi–Yau (CY) manifold known as local P1 × P1 [12, 3].”
Nonperturbative aspects of ABJM theory (2011, methodology): “As pointed in [5, 6], the ABJM matrix model is closely related to that of Chern–Simons theory on S(3)/Z2.”
SUSY gauge theories on squashed three-spheres (2011, background): “It has also been attracting wide attention from various other fields, for example Wilson loops [5, 6], 3D dualities [2], large-N duality of topological string [7] and the ABJM theory at strong coupling [8, 9, 10].”