Noninvertible duality defects in 3 + 1 dimensions

A novel kind of generalized global symmetries is uncovered in a large class of familiar 3+1-dimensional gauge theories, including the free Maxwell theory and Yang-Mills gauge theories. These new symmetries, known as the non-invertible global symmetries, do not have inverses and thus go beyond the traditional paradigm of (anti-)unitary transformations. They are implemented by topological duality defects, generalizing the Kramers-Wannier duality defects in 1+1 dimensions. Remarkably, the existence of certain kinds of duality defects is intrinsically incompatible with a trivially gapped phase and hence gives new constraints on renormalization group flows.

• UD
  U.S. Department of Energy

  Award: DE-SC0021432
• SF
  Simons Foundation