FLAT CURRENTS OF A GREEN–SCHWARZ SIGMA MODEL ON SUPERCOSET TARGETS WITH ℤ4m GRADING

Abstract

We construct actions of Green–Schwarz sigma models on supercoset targets with ℤ4m grading whose kinetic terms only contain the target-space bosons. We consider a simple case of such kinetic term and show that there exist a one-parameter family of flat currents of the model by requiring a suitable choice of the Wess–Zumino term. Such flat currents naturally lead to a hierarchy of classical conserved nonlocal charges. We also find that the one-parameter flat currents of the model satisfy equations of motion and the Virasoro constraint. This implies that one can generate a series of classical solutions from an existing one. When m = 1, our model coincides with the well-known model given by Metsaev and Tseytlin on a supercoset PSU (2, 2|4)/[ SO (4, 1) × SO (5)] and similar models.