Abstract
We investigate the interactions of discrete zero-form and one-form global symmetries in (1+1)d theories. Focus is put on the interactions that the symmetries can have on each other, which in this low dimension result in 2-group symmetries or symmetry fractionalization. A large part of the discussion will be to understand a major feature in (1+1)d: the multiple sectors into which a theory decomposes. We perform gauging of the one-form symmetry, and remark on the effects this has on our theories, especially in the case when there is a global 2-group symmetry. We also implement the spectral sequence to calculate anomalies for the 2-group theories and symmetry fractionalized theory in the bosonic and fermionic cases. Lastly, we discuss topological manipulations on the operators which implement the symmetries, and draw insights on the (1+1)d effects of such manipulations by coupling to a bulk (2+1)d theory.
Highlights
The purpose of this paper is to study theories in (1+1)d that exhibit a discrete global zero-form and one-form symmetry
We investigate the interactions of discrete zero-form and one-form global symmetries in (1+1)d theories
Focus is put on the interactions that the symmetries can have on each other, which in this low dimension result in 2-group symmetries or symmetry fractionalization
Summary
We will build to the definition of a 2-group by introducing some formal definitions from category theory and homotopy theory required to sharply define a 2-group. One could say the collection of zero-form symmetries of a theory is described by a group object in the category Set. We turn to a generalization of groups: groupoids. The objects in this category are groupoids, which are categories themselves, and the morphisms between objects are functors of groupoids We can simplify this generalization to once again recover the traditional notion of a group, which is given by the morphisms in a groupoid. The morphisms of a groupoid with only one object form a group under composition. This is a notion of delooping applied to a group, which categorifies it into a groupoid. We follow the usual slight abuse of notation, taking the space BA as the space that carries a unique group structure that is the underlying group for a 1-form symmetry, and taking BG to be the delooped space which gives the group cohomology of G
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
