  Many different techniques to analyze galaxy clustering data and obtain
cosmological constraints have been proposed, tested and used. Given the large
amount of data that will be available soon, it is worth investigating new
observables and ways to extract information from such datasets. In this paper,
we focus on antisymmetric correlations, that arise in the cross-correlation of
different galaxy populations when the small-scale power spectrum is modulated
by a long-wavelength field. In $\Lambda$CDM this happens because of nonlinear
clustering of sources that trace the underlying matter distribution in
different ways. Beyond the standard model, this observable is sourced naturally
in various new physics scenarios.
  We derive, for the first time, its complete expression up to second order in
redshift space, and show that this improves detectability compared to previous
evaluations at first order in real space. Moreover, we explore a few potential
applications to use this observable to detect models with vector modes, or
where different types of sources respond in different ways to the underlying
modulating long mode, and anisotropic models with privileged directions in the
sky. This shows how antisymmetric correlations can be a useful tool for testing
exotic cosmological models.
