G. 't Hooft presents a gauge theory with a color gauge group \( U(N) \) and quarks having a color index running from 1 to \( N \). In the limit \( N \to \infty \) with \( g^2 N \) fixed, only planar diagrams with quarks at the edges dominate. The topological structure of the perturbation series in \( 1/N \) is identical to that of dual models, where \( 1/N \) corresponds to the dual coupling constant. For hadrons, \( N \) is likely equal to three. A mathematical framework is proposed to link planar diagrams with the functional integrals of Gervais, Sakita, and Mandelstam for the dual string. The paper discusses the singular infrared behavior of massless gauge theories, suggesting that long-range forces can form infinite potential wells for single quarks in hadrons. The Han-Nambu quark theory provides a qualitative picture of these forces, and a formal argument using functional integrals supports the conjecture that "colored" states have infinite energy. The author emphasizes an interesting coincidence: when \( N \) is treated as a free parameter, the expansion of amplitudes at \( N \to \infty \) arranges Feynman diagrams into sets with the topology of the quantized dual string, with quarks at its ends. This analogy is further pursued by writing planar diagrams in the light cone reference frame. A Hamiltonian is formulated to generate all planar diagrams in a Hilbert space of a fixed number of quarks. The quarks are inseparable if and only if the spectrum of this Hamiltonian becomes discrete in the presence of interactions. The paper also explores the comparison between the planar diagram theory and the dual string, and proposes a Hamiltonian formalism to better understand the peculiarities of planar diagram field theory. In conclusion, while a satisfactory theory for bound quarks remains elusive, the planar diagram field theory provides a useful framework. The Han-Nambu theory suggests \( N = 3 \), and the \( 1/N \) expansion is crucial for understanding baryons. If calculations are feasible, the dual coupling constant will be calculable and of order \( \frac{1}{3} \).G. 't Hooft presents a gauge theory with a color gauge group \( U(N) \) and quarks having a color index running from 1 to \( N \). In the limit \( N \to \infty \) with \( g^2 N \) fixed, only planar diagrams with quarks at the edges dominate. The topological structure of the perturbation series in \( 1/N \) is identical to that of dual models, where \( 1/N \) corresponds to the dual coupling constant. For hadrons, \( N \) is likely equal to three. A mathematical framework is proposed to link planar diagrams with the functional integrals of Gervais, Sakita, and Mandelstam for the dual string. The paper discusses the singular infrared behavior of massless gauge theories, suggesting that long-range forces can form infinite potential wells for single quarks in hadrons. The Han-Nambu quark theory provides a qualitative picture of these forces, and a formal argument using functional integrals supports the conjecture that "colored" states have infinite energy. The author emphasizes an interesting coincidence: when \( N \) is treated as a free parameter, the expansion of amplitudes at \( N \to \infty \) arranges Feynman diagrams into sets with the topology of the quantized dual string, with quarks at its ends. This analogy is further pursued by writing planar diagrams in the light cone reference frame. A Hamiltonian is formulated to generate all planar diagrams in a Hilbert space of a fixed number of quarks. The quarks are inseparable if and only if the spectrum of this Hamiltonian becomes discrete in the presence of interactions. The paper also explores the comparison between the planar diagram theory and the dual string, and proposes a Hamiltonian formalism to better understand the peculiarities of planar diagram field theory. In conclusion, while a satisfactory theory for bound quarks remains elusive, the planar diagram field theory provides a useful framework. The Han-Nambu theory suggests \( N = 3 \), and the \( 1/N \) expansion is crucial for understanding baryons. If calculations are feasible, the dual coupling constant will be calculable and of order \( \frac{1}{3} \).