I read that in condensed matter field theory a symmetry implies not only a conserved current (through the well-known Noether theorem) but some kind of "low energy excitation". I am familiar with the symmetries of high energy physics (gauge and space-time symmetries) but not the ones of condensed matter, could some one give me name and maybe more details of one of these symmetries and its low energy excitations.
An example is translational symmetry in solids and phonons. When you break a symmetry by having matter around, like a solid breaking translation symmetry, you can imagine moving a part of the solid slightly and not the rest. The energy cost is only at the boundary between the moved and unmoved part. This means that the energy doesn't scale as the bulk volume, but as the boundary area, and this means that the energy of the excitations per unit volume goes to zero as the wavelength of the excitation gets large.
This is the Goldstone theorem in condensed matter systems--- broken continuous symmetries lead to ungapped excitations.