Note on massless bosonic states in two-dimensional field theories

Abstract

In a wide class of $G_L\times G_R$ 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 $\mathcal{N}=(2,2)$ supersymmetric gauge theory without a superpotential possesses $U(1{)}_L\times U(1{)}_R$ symmetry and contains one massless bosonic state per fixed spatial momentum. The $\mathcal{N}=(4,4)$ supersymmetric pure Yang-Mills theory possesses $SU(2{)}_L\times SU(2{)}_R$ symmetry, and there exist at least three massless bosonic states.

Comments: 17pages, 4 figures, uses PTPTeX.cls and feynMF, added an appendix