  The destruction of Fermi liquid behavior when a gapless Fermi surface is
coupled to a fluctuating gapless boson field is studied theoretically. This
problem arises in a number of different contexts in quantum many body physics.
Examples include fermions coupled to a fluctuating transverse gauge field
pertinent to quantum spin liquid Mott insulators, and quantum critical metals
near a Pomeranchuk transition. We develop a new controlled theoretical approach
to determining the low energy physics. Our approach relies on combining an
expansion in the inverse number (N) of fermion species with a further expansion
in the parameter \epsilon = z_b -2 where z_b is the dynamical critical exponent
of the boson field. We show how this limit allows a systematic calculation of
the universal low energy physics of these problems. The method is illustrated
by studying spinon fermi surface spin liquids, and a quantum critical metal at
a second order electronic nematic phase transition. We calculate the low energy
single particle spectra, and various interesting two particle correlation
functions. In some cases deviations from the popular Random Phase Approximation
results are found. Some of the same universal singularities are also calculated
to leading non-vanishing order using a perturbative renormalization group
calculation at small N extending previous results of Nayak and Wilczek.
Implications for quantum spin liquids, and for Pomeranchuk transitions are
discussed. For quantum critical metals at a nematic transition we show that the
tunneling density of states has a power law suppression at low energies.
