Spectral weight in Chern-Simons theory with symmetry breaking

We calculate the low-energy spectral weight of a holographic superfluid coupled to a Chern-Simons term in IR radial scaling geometries characterized by a parameter eta. This work was motivated by previous results where an unexpected low-energy spectral weight and a region of instability were seen, both at finite momentum, for the holographic superfluid. We characterize the effect of varying the Chern-Simons coupling alpha and condensate charge parameter zeta on these regions supporting low-energy spectral weight or a finite momentum instability. We show that eta, alpha and zeta each plays a unique role in shaping these regions. We find a surface alpha(crit)(eta, zeta) above which the theory is unstable. In the longitudinal channel we extend our analysis to general dimension d. We briefly analyze the Einstein-Maxwell-dilaton theory and find that Fermi shells exist for d > 4.