  We study theoretically quantum melting transitions of stripe order in a
metallic environment, and the associated reconstruction of the electronic Fermi
surface. We show that such quantum phase transitions can be continuous in
situations where the stripe melting occurs by proliferating pairs of
dislocations in the stripe order parameter without proliferating single
dislocations. We develop an intuitive picture of such phases as "Stripe Loop
Metals" where the fluctuating stripes form closed loops of arbitrary size at
long distances. We obtain a controlled critical theory of a few different
continuous quantum melting transitions of stripes in metals . At such a
(deconfined) critical point the fluctuations of the stripe order parameter are
strongly coupled, yet tractable. They also decouple dynamically from the
Fermi-surface. We calculate many universal properties of these quantum critical
points. In particular we find that the full Fermi-surface and the associated
Landau quasiparticles remain sharply defined at the critical point. We discuss
the phenomenon of Fermi surface reconstruction across this transition and the
effect of quantum critical stripe fluctuations on the superconducting
instability. We study possible relevance of our results to several phenomena in
the cuprates.
