Comments on the slope function

The exact slope function was first proposed in $SL(2)$ sector and generalized to $SU(2)$ sector later. In this note, we consider the slope function in $SU(1|1)$ sector of ${\cal N}=4$ SYM. We derive the quantity through the method invented by N. Gromov and discuss about its validity. Further, we give comments on the slope function in deformed SYM.