Measuring the net circular polarization of the stochastic gravitational
  wave background with interferometers
  Parity violating interactions in the early Universe can source a stochastic
gravitational wave background (SGWB) with a net circular polarization. In this
paper, we study possible ways to search for circular polarization of the SGWB
with interferometers. Planar detectors are unable to measure the net circular
polarization of an isotropic SGWB. We discuss the possibility of using the
dipolar anisotropy kinematically induced by the motion of the solar system with
respect to the cosmic reference frame to measure the net circular polarization
of the SGWB with planar detectors. We apply this approach to LISA, re-assessing
previous analyses by means of a more detailed computation and using the most
recent instrument specifications, and to the Einstein Telescope (ET),
estimating for the first time its sensitivity to circular polarization. We find
that both LISA and ET, despite operating at different frequencies, could detect
net circular polarization with a signal-to-noise ratio of order one in a SGWB
with amplitude $h^2 \Omega_\text{GW} \simeq 10^{-11}$. We also investigate the
case of a network of ground based detectors. We present fully analytical,
covariant formulas for the detector overlap functions in the presence of
circular polarization. Our formulas do not rely on particular choices of
reference frame, and can be applied to interferometers with arbitrary angles
among their arms.
