Note on massless bosonic states in two-dimensional field theories

In a wide class of G(L) x G(R) invariant two-dimensional super-renormalizable field theories, the parity-odd part of the two-point function of global currents is completely determined by a fermion one-loop diagram. For any non-trivial fermion content, the two-point function possesses a massless pole which corresponds to massless bosonic physical states. As an application, we show that two-dimensional N = (2,2) supersymmetric gauge theory without a superpotential possesses U(1)(L) X U(1)(R) symmetry and contains one massless bosonic state per fixed spatial momentum. The N = (4,4) supersymmetric pure Yang-Mills theory possesses SU(2)(L) x SU(2)(R) symmetry, and there exist at least three massless bosonic states.