13 - The baryonic spectrum of multiflavor QCD₂ in the strong coupling limit

Summary

We are now going to compute the baryonic spectrum of QCD₂, for which as it turns out the bosonic formulation is very convenient. The mesonic spectrum was found earlier, using large N with quark fields as variables in Chapter 10, as well as using currents as building blocks in Section 11.3. For the baryon spectrum, however, the large N limit, in terms of fermionic fields, is not the natural framework to use since in such a picture the baryon is a bound state of a large number N of constituents. Instead, it will be shown in this chapter that the bosonized version of QCD₂ in the strong coupling limit provides an effective description of the baryons. We will start by deriving the effective action at the strong coupling limit. It will be argued that for the purpose of extracting the low-lying baryons, one can in fact use the product scheme instead of the U(N_c × N_c) scheme, with the former being more suitable for our purposes. Once the effective action is written down we will search for soliton solutions that carry a baryon number. It will be shown that for a static configuration the effective action reduces to a sum of sine-Gordon actions. Using the knowledge acquired on solitons, in Chapter 5, it will be easy to write down the classical baryonic configuration. We will then semi-classically quantize these solitons.