Nonperturbative aspects of ABJM theory

By N. Drukker, Marcos Mariño, Pavel Putrov. 2011

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A bstractUsing the matrix model which calculates the exact free energy of ABJM theory on $ {\mathbb{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 AdS4 × $ \mathbb{C}{\mathbb{P}^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 $ \mathbb{R}{\mathbb{P}^3} $.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/8303df45fa556924f31aa4edc8837f253656bfdf

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Citations in the corpus

Supersymmetric gauge theories on the five-sphere (2012, methodology): “ition function for 5d SUSY gauge theories on S5 will serve as a more direct measure of the degrees of freedom, like the 3d counterpart which was successfully applied to the case of multiple M2-branes [16, 17, 18]. In this paper, we construct the (Euclidean) ﬁve-dimensional N = 1 SUSY gauge theory on”
Exact results on the ABJM Fermi gas (2012, methodology): “In [14, 17] it was noticed that there are two kinds of non-perturbative instanton effects contributing to the free energy.”
A one-loop test of quantum supergravity (2012, methodology): “For these theories, the partition function at all orders in 1/N was computed in [3, 4] by generalizing earlier work in [5, 6, 7, 8].”
Summing up all genus free energy of ABJM matrix model (2011, methodology): “As demonstrated by Drukker, Mariño, and Putrov [9, 11, 10], the free energy can be calculated for arbitrary ’t Hooft coupling λ and order by order in the 1/N expansion.”
ABJM theory as a Fermi gas (2011, methodology): “Finally, building on the results of [5, 8], it was shown in [9] that, once worldsheet instantons are discarded, the full free energy of the ABJM matrix model is given by an Airy function.”
Non-perturbative effects and the refined topological string (2013, background): “These effects were anticipated in [9], where they were interpreted as membrane instanton effects in M-theory, or equivalently as D2-brane effects in type IIA theory.”
Lectures on localization and matrix models in supersymmetric Chern–Simons-matter theories (2011, background): “ce it amounts to solving for the free energy of the dual type IIA superstring theory at all genera. This also makes it possible to address interesting nonperturbative questions in the genus expansion [30]. 9.2 More general Chern{Simons{matter theories In these lectures we have only considered the AB”
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].”
Lectures on non‐perturbative effects in large N gauge theories, matrix models and strings (2012, background): “This picture of instanton actions as periods of the spectral curve, pointed out in [52], seems to be the most general framework explaining the large order structure of a very general class of”
Topological Strings from Quantum Mechanics (2014, background): “However, there are additional non-perturbative corrections which were first pointed out in [4] and then uncovered in a series of papers [5, 6, 7, 8, 9, 10, 11].”
Instanton bound states in ABJM theory (2013, background): “From the viewpoint of the Type IIA string theory on AdS4 × CP 3, which is holographically dual to the ABJM theory in the ’t Hooft limit, the worldsheet instanton comes from the fundamental string wrapping the holomorphic cycle CP1 ⊂ CP3 [6, 20], while the membrane instanton comes from the D2-brane w”
A primer on resurgent transseries and their asymptotics (2018, background): “, [180, 176, 181, 164, 97, 16, 210, 80] for large N gauge theories, and, e.”
Rigid supersymmetric theories in curved superspace (2011, background): “Even though we do not discuss it here in detail, it is clear that the same issue with lack of reflection positivity applies to non-conformal N = 2 theories on S(4) [1-3] and on S(3) [4-20].”
Instanton effects in ABJM theory from Fermi gas approach (2012, methodology): “worldsheet instanton comes from the fundamental string wrapping the holomorphic cycle CP 1 ⊂ CP(3) [6, 15], while the D2-instanton comes from the D2-brane wrapping the Lagrangian submanifold RP(3) ⊂ CP(3) [16].”