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):