Recently I’ve been interested in extended observables in gapless theories. Examples of such non-local observables include Wilson loop operators in gauge theories and disorder operators (also known as defects) in theories with global symmetry. In fact, the Renyi entanglement entropy is also an example of disorder operator. Correlation functions of such operators may reveal new universal properties of the theory, which escape the grasps of local observables.
Symmetric topological phases
Classifications of symmetry-protected and symmetry-enriched topological phases in both two and three spatial dimensions.