nLab large 1/N limit

Idea

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

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

References

General

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

• Leonard Susskind, Another Conjecture about M(atrix) Theory (arXiv:hep-th/9704080)

  (in the context of the BFSS matrix model)

• Nissan Itzhaki, Juan Maldacena, Jacob Sonnenschein, Shimon Yankielowicz, Supergravity and The Large $N$ Limit of Theories With Sixteen Supercharges, Phys. Rev. D 58, 046004 (1998) (arXiv:hep-th/9802042)

  (phase diagrams in $N_c$ and 't Hooft coupling for various Dp-brane species)

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:

• Dror Bar-Natan, Lie Algebras and the Four Color Theorem, Combinatorica 17-1(1997) 43–52 (arXiv:q-alg/9606016, doi:10.1007/BF01196130)

In AdS/CFT

General

• 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 $1/N$ 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 $AdS_2$ (arXiv:1912.07606)

Via conformal bootstrap

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

• Nathan B. Agmon, Shai Chester, Silviu S. Pufu, Solving M-theory with the Conformal Bootstrap, JHEP 06 (2018) 159 (arXiv:1711.07343)

• Shai Chester, Bootstrapping M-theory, 2018 (pdf)

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

• Shai Chester, Eric Perlmutter, M-Theory Reconstruction from $(2,0)$ CFT and the Chiral Algebra Conjecture, J. High Energ. Phys. (2018) 2018: 116 (arXiv:1805.00892)

• Luis Alday, Shai Chester, Himanshu Raj, 6d $(2,0)$ and M-theory at 1-loop (arXiv:2005.07175)

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

• Nathan B. Agmon, Shai Chester, Silviu S. Pufu, The M-theory Archipelago (arXiv:1907.13222)

Specifically in AdS5/CFT4 via D3-brane contributions:

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

In AdS/QCD

Discussion of small N corrections specifically in holographic QCD:

• B. Basso, Cusp anomalous dimension in planar maximally supersymmetric Yang-Mills theory, Continuous Advances in QCD 2008, pp. 317-328 (2008) (spire:858223, doi:10.1142/9789812838667_0027)

  “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.”

• H. Dorn, H.-J. Otto, On Wilson loops and $Q\bar Q$-potentials from the AdS/CFT relation at $T\geq 0$, In: A. Ceresole, C. Kounnas , Dieter Lüst, Stefan Theisen (eds.) Quantum Aspects of Gauge Theories, Supersymmetry and Unification Lecture Notes in Physics, vol 525. Springer 2007 (arXiv:hep-th/9812109, doi:10.1007/BFb0104268)

• Masayasu Harada, Shinya Matsuzaki, and Koichi Yamawaki, Implications of holographic QCD in chiral perturbation theory with hidden local symmetry, Phys. Rev. D 74, 076004 (2006) (doi:10.1103/PhysRevD.74.076004)

  (with an eye towards hidden local symmetry in chiral perturbation theory)

• Csaba Csaki, Matthew Reece, John Terning, The AdS/QCD Correspondence: Still Undelivered, JHEP 0905:067, 2009 (arXiv:0811.3001)

• Salvatore Baldino, Stefano Bolognesi, Sven Bjarke Gudnason, Deniz Koksal, A Solitonic Approach to Holographic Nuclear Physics, Phys. Rev. D 96, 034008 (2017) (arXiv:1703.08695)

In 2d QCD

On 1/N corrections in 2d QCD:

• Itzhak Bars, QCD and Strings in 2D (arXiv:hep-th/9312018)