nLab
large 1/N limit

Contents

Context

Quantum Field Theory

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

Introduction

Concepts

field theory:

Lagrangian field theory

quantization

quantum mechanical system, quantum probability

free field quantization

gauge theories

interacting field quantization

renormalization

Theorems

States and observables

Operator algebra

Local QFT

Perturbative QFT

String theory

Contents

Idea

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:

References

General

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:

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/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

In AdS/QCD

Discussion of small N corrections specifically in holographic QCD:

In 2d QCD

On 1/N corrections in 2d QCD:

Last revised on May 15, 2020 at 02:38:48. See the history of this page for a list of all contributions to it.