Decomposition squared

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.

30 pages, LaTeX, v2: discussion of more general levels added

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Cited by in corpus (3)

• One-form symmetries and the 3d $\mathcal{N}=2$ $A$-model: Topologically twisted indices and CS theories
• Schubert line defects in 3d GLSMs, part II: Partial flag manifolds and parabolic quantum polynomials
• Schubert line defects in 3d GLSMs, part I: Complete flag manifolds and quantum Grothendieck polynomials