Supersymmetric Yang-Mills Theories in 1 + 1 Dimensions

Supersymmetric Yang-Mills theories are considered in 1+1 dimensions. Firstly physical mass spectra of supersymmetric Yang-Mills theories in 1+1 dimensions are evaluated in the light-cone gauge with a compact spatial dimension. The supercharges are constructed in order to provide a manifestly supersymmetric infrared regularization for the discretized light-cone approach. By exactly diagonalizing the supercharge matrix between up to several hundred color singlet bound states, we find a rapidly increasing density of states as mass increases. Interpreting this limiting density of states as the stringbehavior, we obtain the Hagedron temperature $\beta_H=0.676 \sqrt{\pi \over g^2 N}$. Secondly we have examined the vacuum structure of supersymmetric Yang-Mills theories in 1+1 dimensions. SUSY allows only periodic boundary conditions for both fermions and bosons. By using the Born-Oppenheimer approximation for the weak coupling limit, we find that the vacuum energy vanishes, and hence the SUSY is unbroken. Other boundary conditions are also studied. The first part is based on a work in collaboration with Y. Matsumura and T. Sakai. The second part is based on a work in collaboration with H. Oda and T. Sakai.