TL;DR
This paper explores how certain three-dimensional theories with one-form symmetries decompose under specific conditions, extending conjectures in quantum K theory using advanced mathematical and physical tools.
Contribution
It extends the application of decomposition to three-dimensional theories with one-form symmetries and quantum K theory, providing new insights and conjectures.
Findings
Decomposition occurs in OPEs of line operators and dimensional reductions.
Extended conjectures for quantum K theory rings of gerbes.
Applied decomposition to orbifold partition functions and gauged linear sigma models.
Abstract
In this paper, we test and extend a proposal of Gu, Pei, and Zhang for an application of decomposition to three-dimensional theories with one-form symmetries and to quantum K theory. The theories themselves do not decompose, but, OPEs of parallel one-dimensional objects (such as Wilson lines) and dimensional reductions to two dimensions do decompose, sometimes in two independent ways. We apply this to extend conjectures for quantum K theory rings of gerbes (realized by three-dimensional gauge theories with one-form symmetries) via both orbifold partition functions and gauged linear sigma models.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Black Holes and Theoretical Physics