Action

#### 1` `Parametrization of

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 .

#### 2` `Action

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: