Momentum space correlators in parity-violating CFT3

Abstract

Conformal field theory in momentum space has a wide range of applications but has been studied much lesser compared to its position space counterpart. In this thesis, we calculate momentum space 3- point functions in a general parity-violating CFT3. We do this using four techniques - solving conformal Ward identities in momentum space, solving conformal Ward identities in spinor-helicity variables, using weight shifting operators and by computing tree level amplitudes in dS4. These techniques have been used before to calculate parity-even correlation functions involving scalars, spin -1 and spin -2 currents. We note the using spinor-helicity variables provides a natural splitting of the correlation function into a homogeneous and inhomogeneous part and upon doing so, we solve for the homogeneous part of correlators involving conserved currents of arbitrary spin. After obtaining the correlators, we see that all correlators have at most 2 parity-even and one parity-odd structure upto contact terms. Then, we demonstrate that a double copy structure for 3- point functions exists in a general parity-violating CFT. We also make connections between CFT correlators and flat space amplitudes and show that the double copy structure for the amplitudes holds beyond the flat space limit.