Comments on the slope function

TL;DR

This paper explores the slope function in the $SU(1|1)$ sector of ${ m ext{N}=4}$ SYM, deriving it using Gromov's method and discussing its validity and implications for deformed SYM theories.

Contribution

It extends the analysis of the slope function to the $SU(1|1)$ sector and evaluates the method's validity, also commenting on deformed SYM cases.

Findings

Derived the slope function in $SU(1|1)$ sector using Gromov's method

Discussed the validity of the derived slope function

Commented on the slope function in deformed SYM theories

Abstract

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.