nLab large 1/N limit



Quantum Field Theory

algebraic quantum field theory (perturbative, on curved spacetimes, homotopical)



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In the context of the 't Hooft double line construction and the AdS/CFT correspondence with N cN_c \in \mathbb{N} colors, the small NN region or large 1/N c1/N_c limit is the situation away from the large N limit. In this large 1/N c1/N_c limit perturbative string theory-corrections (for small 't Hooft coupling λ=g YM 2N c\lambda = g_{YM}^2 N_c) and/or M-theory-corrections (for small N c N_c ) to the supergravity-approximation of the AdS/CFT correspondence are relevant.

In application to phenomenology, the small N cN_c region (and hence M-theory) is what is ultimately relevant for the AdS/QCD correspondence, given that quantum chromodynamics has a small number N c QCD=3N_c^{QCD} = 3 of quark colors:



On the general relevance of M-theory at small N cN_c in gauge/gravity duality:

On the logical equivalence between the four-colour theorem and a statement about transition from the small N limit to the large N limit for Lie algebra weight systems on Jacobi diagrams via the 't Hooft double line construction:



  • B. Basso, Cusp anomalous dimension in planar maximally supersymmetric Yang-Mills theory (spire:858223)

    “The result [[(29)]] coincides exactly with the recent two-loop stringy correction computed in Alday-Maldacena 07, providing a striking confirmation of the AdS/CFT correspondence.”

  • David Jorrin, Nicolas Kovensky, Martin Schvellinger, Towards 1/N1/N corrections to deep inelastic scattering from the gauge/gravity duality, JHEP 04 (2016) 113 (arXiv:1601.01627)

Discussion of small N corrections via a lattice QFT-Ansatz on the AdS side of AdS2/CFT1:

  • Richard C. Brower, Cameron V. Cogburn, A. Liam Fitzpatrick, Dean Howarth, Chung-I Tan, Lattice Setup for Quantum Field Theory in AdS 2AdS_2 (arXiv:1912.07606)

Via conformal bootstrap

Using the conformal bootstrap for CFTs at small N to deduce M-theory-properties on the dual side:

Specifically for the D=6 N=(2,0) SCFT on the M5-brane via AdS7/CFT6:

Specifically for the D=3 SCFT (BLG-model, ABJM model) on the M2-brane via AdS4/CFT3

Specifically in AdS5/CFT4 via D3-brane contributions:

  • Yosuke Imamura, Finite-NN superconformal index via the AdS/CFT correspondence (arXiv:2108.12090)


Discussion of small N corrections specifically in holographic QCD:

In 2d QCD

On 1/N corrections in 2d QCD:

Last revised on July 12, 2023 at 18:54:48. See the history of this page for a list of all contributions to it.