Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Topological operators, noninvertible symmetries and decomposition   In this paper we discuss the relationship between noninvertible topological
operators, one-form symmetries, and decomposition of two-dimensional quantum
field theories, focusing on two-dimensional orbifolds with and without discrete
torsion. As one component of our analysis, we study the ring of dimension-zero
operators in two-dimensional theories exhibiting decomposition. From a
commutative algebra perspective, the rings are naturally associated to a finite
number of points, one point for each universe in the decomposition. Each
universe is canonically associated to a representation, which defines a
projector, an idempotent in the ring of dimension-zero operators. We discuss
how Wilson lines on boundaries of two-dimensional theories decompose, and
compute actions of projectors. We discuss one-form symmetries of the rings, and
related properties. We also give general formulas for projection operators,
which previously were computed on a case-by-case basis. Finally, we propose a
characterization of noninvertible higher-form symmetries in this context in
terms of representations. In that characterization, non-isomorphic universes
appearing in decomposition are associated with noninvertible one-form
symmetries.

1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
16
The categories of this paper are: stat
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con