Amplitudes Seminar

(Super)Conformal Theories in Momentum space and Spinor Helicity Variables [Zoom Talk]

by Shivang Yadav (IISER Pune)

Traditionally, CFTs are studied in position space, while scattering amplitudes are analyzed in momentum space. Thus, studying CFTs directly in momentum space naturally connects these approaches. The prominent method involves spinor helicity variables, which we extended to three-dimensional Superconformal Field Theories (SCFTs) using new variables called Grassmann Twistor Variables. We found the exact functional form of all spinning SCFT correlators and uncovered new relations between CFT correlators in these variables.

However, these insights are mostly limited to three-point functions, as higher-point functions involve complex vector differential equations. To tackle this, we explored one-dimensional systems, showing that n-point functions in one-dimensional momentum space can be expressed as Lauricella functions. This provides a closed functional form for n-point functions, thus paving the way for advancements in higher-dimensional CFT studies.