  In this paper, we present our studies of the phase diagram of the cuprate
superconductors performed in recent years. We describe how a few
field-theoretical concepts can be used to account for the puzzling properties
of these compounds. Starting with a short exposition of recent experimental
developments, we then introduce the concept of an emergent SU(2) symmetry,
which rotates between the superconducting and charge order parameters. We
describe a solvable model for which this symmetry turns out to be exact and
derive the corresponding effective field theory in terms of a non-linear
{\sigma} model. We then turn to the experimental consequences of our model with
the presence of skyrmions inside the vortex core and an elegant account of the
B-T phase diagram. Next, we move on to the second concept, which is the one of
an emergent U(1) gauge field in the theory. Within this more general framework,
the pseudogap transition can be viewed as a confining/deconfining transition.
Experimental consequences for a few spectroscopic probes like inelastic neutron
scattering, Raman spectroscopy, phonon line in x-ray scattering and
angle-resolved photoemission experiments are studied. This theory suggests the
presence of incoherent bosons at moderate temperatures in the phase diagram of
the cuprates, which would undergo a jamming transition at optimal doping [1].
Consequences of the presence of such bosons on the transport properties of
these materials are examined.
