Starting from Witten's large-$N$ power counting we derive an equation identical to the so-called bootstrap condition of strong-coupling theory. The large-$N$ baryons are therefore characterized by representations of the strong-coupling group (SCG). It is pointed out that the bootstrap relation is quite general and valid when the semiclassical expansion about soliton solutions is at work. The collective coordinates of the soliton correspond to the coordinates of induced representations of the SCG. One of the interesting representations of the SCG is the quark representation and this makes a bridge between the Skyrme solitons and the nonrelativistic quark model. We explicitly show that the induced representation is derived from $N$ static quarks with $N\to \infty$. We further emphasize the generality and power of the algebraic method. For this purpose we present a modified chiral bag model which exhibits the algebraic relations in large $N$ and approaches the Skyrme-soliton picture in the zero-bag-radius limit.

• Received 1 March 1984

DOI:https://doi.org/10.1103/PhysRevD.30.1795