The complex interactions involving highly correlated electron systems can give rise to “exotic behavior” in electronic systems, such as quantum criticality and superconductivity. The usual theoretical tools, however, are limited when describing these states. String theory is a highly mathematical approach initially developed to describe gravity and high-energy particle physics. Certain aspects of string theory may be relevant to describe condensed matter systems. Cubrovic et al. (p. [439][1]; published online 25 June) take one such approach, and show that the characteristic properties of a Fermi liquid can emerge from string theory. The formulation may provide an approach to describing the exotic states of matter that arise in condensed matter systems.
[1]: /lookup/volpage/325/439
We review recent progress and a number of future directions for applications of effective field theory methods to condensed matter systems broadly defined. Our emphasis is on areas that have allowed a fertile exchange of ideas between high energy physics and many-body theory. We discuss developments in the effective field theory of spontaneous symmetry breaking, of hydrodynamics and non-equilibrium dynamics more generally, fracton phases of matter, and dualities between 2+1 dimensional field theories. We furthermore discuss the application of effective field theory to non-Fermi liquids, the dynamics of entanglement entropy and to condensed matter aspects of cosmology.
Global symmetry (0-symmetry) acts on the whole space while higher
k-symmetry acts on all the codimension-
k closed subspaces. The usual condensed matter lattice theories do not include dynamical electromagnetic (EM) field and do not have higher symmetries (unless we engineer fine-tuned toy models). However, for gapped systems, (anomalous) higher symmetries can emerge from the usual condensed matter theories at low energies (usually in a spontaneously broken form). We pointed out that the emergent spontaneously broken higher symmetries are nothing but a kind of topological order. Thus the study of emergent spontaneously broken higher symmetries is a study of topological order. The emergent (anomalous) higher symmetries can be used to constrain possible phase transitions and possible phases induced by certain types of excitations in topological orders. (Anomalous) higher symmetry can also emerge in gapless systems if the gapless excitations contain gapless gauge fields. In particular, EM condensed matter systems that include the dynamical EM field have an emergent anomalous
U(1)-1-symmetry below the energy gap of the magnetic monopoles. So EM condensed matter systems can realize some physical phenomena of anomalous higher symmetry. In particular, any gapped liquid phase of an EM condensed matter system (induced by arbitrary fluctuations and condensations of electric charges and photons) must have a nontrivial bosonic topological order.