nLab 't Hooft coupling

Idea

In Yang-Mills theory/QCD with coupling constant $g_{YM}$ and with $N_c$ colours, the ’t Hooft coupling is the expression

$$\lambda \;\coloneqq\; g_{YM}^2 N_c \,.$$

Properties

In the large $N$ limit

The study of Yang-Mills theory in the large N limit but at fixed ’t Hooft coupling controls the AdS/CFT correspondence:

large N limit$\;N_c \to \infty$ at fixed 't Hooft coupling $\lambda = g_{YM}^2 N_c$

$\lambda \lt 1$	$\lambda \gt 1$
small coupling limit of Yang-Mills theory	low-energy supergravity limit of string theory on asymptotically AdS spacetime

(e. g. Aharony-Gubser-Maldacena-OoguriOz 99, p. 11, p. 60, Nastase 07, Section 8)

(…)

Related concepts

• large N limit

• AdS/CFT

References

The original article

• Gerard 't Hooft, A Planar Diagram Theory for Strong Interactions, Nucl. Phys. B72 (1974) 461 (spire:80491, doi:10.1016/0550-3213(74)90154-0)

Review:

• Ofer Aharony, Steven Gubser, Juan Maldacena, Hirosi Ooguri, Yaron Oz, Large $N$ Field Theories, String Theory and Gravity, Phys. Rept. 323 183-386 (2000) $[$doi:10.1016/S0370-1573(99)00083-6, arXiv:hep-th/9905111$]$

• Horatiu Nastase, Introduction to AdS-CFT (arXiv:0712.0689)