The apparent distribution of large-scale structures in the universe is sensitive to the velocity/potential of the sources as well as the potential along the line-of-sight through the mapping from real space to redshift space (redshift-space distortions, RSD). Since odd multipoles of the halo cross-correlation function vanish when considering standard Doppler RSD, the dipole is a sensitive probe of relativistic and wide-angle effects. We build a catalogue of ten million haloes (Milky-Way size to galaxy-cluster size) from the full-sky light-cone of a new "RayGalGroupSims" N-body simulation which covers a volume of (2.625 h −1 Gpc) 3 with 4096 3 particles. Using ray-tracing techniques, we find the null geodesics connecting all the sources to the observer. We then selfconsistently derive all the relativistic contributions (in the weak-field approximation) to RSD: Doppler, transverse Doppler, gravitational, lensing and integrated Sachs-Wolfe. It allows us, for the first time, to disentangle all contributions to the dipole from linear to non-linear scales. At large scale, we recover the linear predictions dominated by a contribution from the divergence of neighbouring line-of-sights. While the linear theory remains a reasonable approximation of the velocity contribution to the dipole at non-linear scales it fails to reproduce the potential contribution below 30 − 60 h −1 Mpc (depending on the halo mass). At scales smaller than ∼ 10 h −1 Mpc, the dipole is dominated by the asymmetry caused by the gravitational redshift. The transition between the two regimes is mass dependent as well. We also identify a new non-trivial contribution from the non-linear coupling between potential and velocity terms.
We study the general deformation of N = 2 supersymmetry transformations of a vector multiplet that forms a (constant) triplet under the SU (2) R-symmetry corresponding to the magnetic dual of the triplet of the Fayet-Iliopoulos (FI) parameters. We show that in the presence of both triplets, the induced scalar potential of a vector multiplet with generic prepotential has always a minimum that realises partial breaking of N = 2 → N = 1 supersymmetry. We then consider the impact of the deformation in the Dirac-Born-Infeld (DBI) action where one supersymmetry is non-linearly realised, described by a nilpotent constraint on the deformed N = 2 chiral-chiral superfield. We show that the generic magnetic deformation induces an ordinary FI D-term along the linear supersymmetry via the theta-angle. Moreover, we argue that the resulting action differs on-shell from the standard one (DBI+FI) by fermionic contributions.
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