Instabilities of 2d quantum critical metals in the N_f→0 limit

We study a Fermi surface coupled to fluctuations of one or more critical order parameters in 1+2 dimensions. The limit of vanishing fermion flavor number gives a controlled way of studying this strongly coupled theory. In this talk I show results for charge, spin and pairing susceptibilities and find that the critical fluctuations may induce charge/spin density wave order or pairing depending on the types of critical order parameter fluctuations and their interplay.