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On-shell Methods for Form Factors in N=4 SYM and Their Applications

Form factors are quantities that involve both asymptotic on-shell states and gauge invariant operators. They provide a natural bridge between on-shell amplitudes and off-shell correlation functions of operators, thus allowing us to use modern on-shell amplitude techniques to probe into the off-shell side of quantum field theory. In particular, form factors have been successfully used in computing the cusp (soft) anomalous dimensions and anomalous dimensions of general local operators. This review is intended to provide a pedagogical introduction to some of these developments. We will first review some amplitudes background using four-point amplitudes as main examples. Then we generalize these techniques to form factors, including (1) tree-level form factors, (2) Sudakov form factor and infrared singularities, and (3) form factors of general operators and their anomalous dimensions. Although most examples we consider are in N=4 super-Yang-Mill theory, the on-shell methods are universal and are expected to be applicable to general gauge theories.