Starting from the large-AT power counting which suggests that the baryons are QCD solitons, the authors derive an exact large-TV equation identical to the so-called bootstrap condition of static strong-coupling theory. This equation determines the group structure of the baryon multiplets at JV-*°°.. One solution is the standard nonrelativistic quark model. PACS numbers: 12.35.Eq, il.30.Na, 12.40.Ff Some time ago Witten 1 suggested that baryons can be considered as solitons in the large-i\F limit of QCD, This was partially realized in more recent works. 2 These works suggest that the large-N limit could be studied as a sort of semiclassical approximation where ft is replaced by 1/N. However, it seems impossible to derive from first principles a concrete baryonlike solution, which is needed as the starting point of the corresponding 1/N expansion. Fortunately we already know one example of a theory where the essential results of semiclassical expansion were derived without making use of the classical solution, This is the so-called static strong-coupling theory of the meson-nucleon interactions. Many well-known physicists 3 have attached their names to the corresponding semiclassical expansion. On the other hand most of the results were later derived by Goebel 4 by means of an S-matrix bootstrap strong-coupling approach, in which no concept of field appears, not to mention any classical solution* Looking back at this approach 4,5 and in view of later studies of the strong-coupling theory 6 and of the more recent developments of semiclassical methods 7 in general, we realized that Goebel's viewpoint is certainly quite general.It provides an alternative route to semiclassical expansions where no classical solution is needed, which we plan to follow in this paper to study the large-Af QCD baryon dynamics. We shall follow closely the method of Ref. 5, where one of the essential ingredients is the behavior of various physical quantities in the strongcoupling limit. We now point out that this behavior is precisely the one which follows from the general arguments of Witten 1 in the large-N QCD. First the baryon mass is proportional to N so that we can use the nonrelativistic kinematics for baryons. On the other hand the meson mass is finite and mesons are fully relativistic. We further need the order of magnitude of the mesonbaryon Yukawa coupling. By a simple quark counting one can see that the corresponding nonrelativistic overlap integral of meson-baryonbaryon wave functions is of order v5v. This agrees with the standard behavior of the mesonsoliton vertex in the semiclassical expansion. 7 Consider the meson-baryon scattering: "a" + "i" -"0 " + "j ", where a and |3 indicate the initial and the final mesons, respectively, while i andj are baryon states. The dispersion relation of the corresponding scattering amplitude can be
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-+ CC. 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 Nand approaches the Skyrme-soliton picture in the zero-bag-radius limit.
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