Shift transformations
Exist such that ; in other words:

Explicitly, they are given by the following formula (cf. Eq. (61) of Berkovits and Howe):

with an arbitrary parameter . Observe that:

The modification does not change

Similarly, we can modify by adding to it some defined in a similar way; we stress that takes values in and takes values in . Obviously, these “shift gauge transformations” depend on two parameters: and . In terms of Eq. (7):