  The entanglement entropy in theories with a Fermi surface is known to produce
a logarithmic violation of the usual area law behavior. We explore the
possibility of producing this logarithmic violation holographically by
analyzing the IR regions of the bulk geometries dual to such theories. The
geometry of Ogawa, Takayanagi, and Ugajin is explored and shown to have a null
curvature singularity for all values of parameters, except for dynamical
critical exponent 3/2 in four dimensions. The results are extended to general
hyperscaling violation exponent. We explore strings propagating through the
singularity and show that they become infinitely excited, suggesting the
singularity is not resolved by stringy effects and may become a full-fledged
"stringularity." An Einstein-Maxwell-dilaton embedding of the nonsingular
geometry is exhibited where the dilaton asymptotes to a constant in the IR. The
unique nonsingular geometry in any given number of dimensions is proposed as a
model to study the T=0 limit of a theory with a Fermi surface.
