Superconformal Field Theories: A Momentum Space Voyage

Abstract

This thesis aims to find correlators in conformal and superconformal field theories in momentum space. In this direction, we studied the implication of conformal invariance in Conformal Quantum Mechanics. This analysis provides the first instance of a closed form for generic momentum space conformal correlators in contrast to higher dimensions. We found that n-point functions in 1 dimensions can be mapped to Lauricella Functions, E_A, with n − 3 undetermined parameters. We test our expressions against free theory and DFF model correlators, finding an exact agreement. Further, we show that multiple solutions to the momentum space conformal ward identity can be attributed to the Fourier transforms of the various possible time orderings. We extend our analysis to theories with N = 1, 2 supersymmetry. Moreover, we develop the first momentum superspace formalism for N = 1, 2 superconformal field theories in 3 dimensions. This formalism comprises new variables, “Super Spinor Helicity” and “Grassmann Twistor Variables”. Using this formalism, we first compute all three point correlation functions involving conserved super-currents with arbitrary spins in N = 1, 2 theories. We discover interesting double copy relations in N = 1 super-correlators. Also, we discovered super double copy relations that take us from N = 1 to N = 2 super-correlators.