Localization and large N reduction on for the planar and M-theory limit

Honda, Masazumi; Yoshida, Yutaka

doi:10.1016/j.nuclphysb.2012.07.022

Cited by 11 publications

(11 citation statements)

References 116 publications

(180 reference statements)

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“…The large-N reduction for N = 4 SYM has been confirmed for the circular Wilson loop to all orders of perturbation theory [73]. More recently, the localization method [25] has been used to demonstrate the large-N reduction for N = 4 SYM [74] and three-dimensional N = 2 theories [75,76].…”

Section: Introductionmentioning

confidence: 90%

Direct test of the AdS/CFT correspondence by Monte Carlo studies of $ \mathcal{N}=4 $ super Yang-Mills theory

Honda

Ishiki

Kim

et al. 2013

J. High Energ. Phys.

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Abstract:We perform nonperturbative studies of N = 4 super Yang-Mills theory by Monte Carlo simulation. In particular, we calculate the correlation functions of chiral primary operators to test the AdS/CFT correspondence. Our results agree with the predictions obtained from the AdS side that the SUSY non-renormalization property is obeyed by the three-point functions but not by the four-point functions investigated in this paper. Instead of the lattice regularization, we use a novel regularization of the theory based on an equivalence in the large-N limit between the N = 4 SU(N ) theory on R × S 3 and a one-dimensional SU(N ) gauge theory known as the plane-wave (BMN) matrix model. The equivalence extends the idea of large-N reduction to a curved space and, at the same time, overcomes the obstacle related to the center symmetry breaking. The adopted regularization for S 3 preserves 16 SUSY, which is crucial in testing the AdS/CFT correspondence with the available computer resources. The only SUSY breaking effects, which come from the momentum cutoff Λ in R direction, are made negligible by using sufficiently large Λ.

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Section: Introductionmentioning

confidence: 90%

Direct test of the AdS/CFT correspondence by Monte Carlo studies of $ \mathcal{N}=4 $ super Yang-Mills theory

Honda

Ishiki

Kim

et al. 2013

J. High Energ. Phys.

Self Cite

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“…Another interesting application can be found in [32,33]. Our construction, oneparameter deformed SUSY on round sphere, guarantees the use of invariant one-forms when we write down the Lagrangians.…”

Section: Discussionmentioning

confidence: 99%

Localization on round sphere revisited

Tanaka

2013

J. High Energ. Phys.

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We consider supersymmetric gauge theories on round 3-sphere with a certain background gauge field. The Lagrangians break the usual symmetry because the background gauge field which we have turned on violates the isometry. In order to maintain the supersymmetry, we choose unfamiliar charged Killing spinors as N = 2 SUSY parameters. We perform localization calculous within this setup and find the double sine function as we expected. We comment on more direct relationship between theories on round sphere and squashed sphere via Weyl transformation.Comment: 17 pages. Weyl rescaling and Wilson loop discussions added. reference adde

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“…There are several observations supporting this assumption, including the Monte Carlo data from the D0-brane matrix quantum mechanics [26,53] and exact calculation of BPS observables based on the localization method [61,36]. 4 Similar calculations [37] suggest that the Eguchi-Kawai equivalence for the supersymmetric Chern-Simons-matter theories [38,39] can be extended to the M-theory region.…”

Section: Introductionmentioning

confidence: 86%

New large-Nlimit and the planar equivalence outside the planar limit

2012

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We consider a new large-N limit, in which the 't Hooft coupling grows with N . We argue that a class of large-N equivalences, which is known to hold in the 't Hooft limit, can be extended to this very strongly coupled limit. Hence this limit may lead to a new way of studying corrections to the 't Hooft limit, while keeping nice properties of the latter. As a concrete example, we describe large-N equivalences between the ABJM theory and its orientifold projection. The equivalence implies that operators neutral under the projection symmetry have the same correlation functions in two theories at large-N . Usual field theory arguments are valid when 't Hooft coupling λ ∼ N/k is fixed and observables can be computed by using a planar diagrammatic expansion. With the help of the AdS/CFT correspondence, we argue that the equivalence extends to stronger coupling regions, N k, including the M-theory region N k 5 . We further argue that the orbifold/orientifold equivalences between certain Yang-Mills theories can also be generalized. Such equivalences can be tested both analytically and numerically. Based on calculations of the free energy, we conjecture that the equivalences hold because planar dominance persists beyond the 't Hooft limit.

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Localization and large N reduction on for the planar and M-theory limit

Cited by 11 publications

References 116 publications

Direct test of the AdS/CFT correspondence by Monte Carlo studies of $ \mathcal{N}=4 $ super Yang-Mills theory

Direct test of the AdS/CFT correspondence by Monte Carlo studies of $ \mathcal{N}=4 $ super Yang-Mills theory

Localization on round sphere revisited

New large-Nlimit and the planar equivalence outside the planar limit

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