Measuring parity violation in the Stochastic Gravitational Wave Background with the LISA-Taiji network

Parity violation is a powerful observable to distinguish a cosmological background of Gravitational Waves (GWs) from an astrophysical one. Planar single GW interferometers, both on ground and in space, are unable to measure the net circular polarization of an isotropic Stochastic Gravitational Wave Background (SGWB). In this paper, we explore the possibility of detecting circular polarization of an isotropic SGWB by cross-correlating two space-based detectors planned to be launched around 2034: LISA and Taiji. We compute the response of such a network to chirality and we perform a Fisher forecast analysis on the $I$ and $V$ Stokes parameters for the SGWB. We find that a clear measurement of chirality can be claimed for a maximally chiral signal with $h^2 \, \Omega_{\rm GW} \simeq 10^{-12}$.