Studying the spectrum of 2D SU(2) gauge theory with a single flavor of massless Majorana fermions

Gauge theory in 2D has been of interest in part because of the appearance of conformal structures. For example, SU(2) gauge theory with massless Dirac fermions is conformal by virtue of a conserved current that obeys a WZW current algebra. The existence of such a current is due to a continuous flavor symmetry which is no longer present when one considers integer spin (J) representations of the gauge group. In this talk we will start with 2D SU(2) gauge theory coupled to one flavor of massless Majorana fermions. Using the Hamiltonian formalism and working in lightcone gauge, we will discuss some curious aspects of the spectrum of this theory. For particular values of J, we find massless modes that are suggestive of a conformal theory in the infrared limit.