Proton spin, topology and confinement: lessons from QCD$_2$

Abstract

We investigate the relation between the topology of a nucleon and its spin composition. We approach this question in (1+1) dimensional single-flavor QCD with a large number of color. In this limit the theory can be shown to be dual to the exactly solvable sine-Gordon model. The spectrum of baryons and mesons is known analytically, and the baryon is a topological kink of the sine-Gordon model. Using the method of solitonic constituents we construct the state of the baryon and extract its $g_1$ structure function. Due to the topological nature of the baryon state this structure function is enhanced at low Bjorken $x$. We propose this enhancement as an experimental probe of the topological structure of the nucleon state.