Anomalously light states in super-Yang–Mills–Chern–Simons theory

Inspired by our previous finding that supersymmetric Yang–Mills–Chern–Simons (SYM–CS) theory dimensionally reduced to 1+1 dimensions possesses approximate Bogomolʹnyi–Prasad–Sommerfield (BPS) states, we study the analogous phenomenon in the three-dimensional theory. Approximate BPS states in two dimensions have masses which are nearly independent of the Yang–Mills coupling and proportional to their average number of partons. These states are a reflection of the exactly massless BPS states of the underlying pure SYM theory. In three dimensions we find that this mechanism leads to anomalously light bound states. While the mass scale is still proportional to the average number of partons times the square of the CS coupling, the average number of partons in these bound states changes with the Yang–Mills coupling. Therefore, the masses of these states are not independent of the coupling. Our numerical calculations are done using supersymmetric discrete light-cone quantization (SDLCQ).