8 research outputs found
Higher Gauging and Non-invertible Condensation Defects
We discuss invertible and non-invertible topological condensation defects
arising from gauging a discrete higher-form symmetry on a higher codimensional
manifold in spacetime, which we define as higher gauging. A -form symmetry
is called -gaugeable if it can be gauged on a codimension- manifold in
spacetime. We focus on 1-gaugeable 1-form symmetries in general 2+1d QFT, and
gauge them on a surface in spacetime. The universal fusion rules of the
resulting invertible and non-invertible condensation surfaces are determined.
In the special case of 2+1d TQFT, every (invertible and non-invertible) 0-form
global symmetry, including the electromagnetic symmetry of the
gauge theory, is realized from higher gauging. We further
compute the fusion rules between the surfaces, the bulk lines, and lines that
only live on the surfaces, determining some of the most basic data for the
underlying fusion 2-category. We emphasize that the fusion "coefficients" in
these non-invertible fusion rules are generally not numbers, but rather 1+1d
TQFTs. Finally, we discuss examples of non-invertible symmetries in
non-topological 2+1d QFTs such as the free Maxwell theory and QED.Comment: 83 page
Asymptotic density of states in 2d CFTs with non-invertible symmetries
It is known that the asymptotic density of states of a 2d CFT in an
irreducible representation of a finite symmetry group is
proportional to . We show how this statement can be generalized
when the symmetry can be non-invertible and is described by a fusion category
. Along the way, we explain what plays the role of a
representation of a group in the case of a fusion category symmetry; the answer
to this question is already available in the broader mathematical physics
literature but not yet widely known in hep-th. This understanding immediately
implies a selection rule on the correlation functions, and also allows us to
derive the asymptotic density.Comment: 42 pages; v2: minor revisio