Besides scattering amplitudes, there are other important physical observables such as the spectrum of operators and correlation functions. Form factors, which contain both on-shell states and local operators, provide a useful bridge to bring the on-shell amplitude techniques to the off-shell world of correlation functions. Amplitudes inspired methods open a new avenue to study this new class of observables as well as offering new insight to understand spin chains and integrability in N=4 SYM.

Single trace operators v.s. Spin chains

• Single trace operators in gauge theories may be related to some spin chain models. For example, the anomalous dilatation operator (or anomalous dimension) is mapped to the spin chain Hamiltonian (or energy). The spin chain models, when integrable, may be exactly solvable, thus can be used to understand the non-perturbative dynamics of gauge theories. This idea has played a significant role in understanding the N=4 SYM as well as the AdS/CFT correspondence. Inspired by the modern amplitudes techniques, it becomes possible to compute the dilation operator via modern spinor helicity and unitarity on-shell methods for arbitrary single trace operators. 

• With Nandan, Wilhelm and Sieg, I initiated the study of form factors with non-protected operators at higher loop order, focusing on the Konishi operator. Since the operator is not protected by supersymmetry, we found its form factors share many features with those in QCD, such as the occurrence of rational terms and of ultraviolet (UV) divergences. We also computed the two-loop total cross section based on the form factor results. (See our paper for more details.)

• In a further project with Loebbert, Nandan, Wilhelm and Sieg, I studied the general single trace operators in the SU(2) sector of N=4 SYM. We obtained the known two-loop dilatation operator and also the two-loop remainder function for the first time. (See our paper for more details.) Such method is not limited to N=4 SYM but may be applied to general gauge theories.