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):