The global symmetry algebra is . It has the grading .
Matter fields are collected into the group element ; the right-invariant currents are defined as follows:
which is invariant under , with a global parameter .
Various worldsheet fields take values in ; the lower index will denote the grade of the field. For example, is the momentum of . The index means that it takes values in , and the index means that it has the conformal dimension ; similarly the field has the conformal dimension and takes values in . The fields are defined as follows: