Complementary Projection Defects and Decompositions

Abstract

As put forward in [arXiv:1907.12339] topological quantum field theories can be projected using so-called projection defects. The projected theory and its correlation functions can be completely realized within the unprojected one. An interesting example is the case of topological quantum field theories associated to IR fixed points of renormalization group flows, which by this method can be realized inside the theories associated to the UV. In this note we show that projection defects in triangulated defect categories (such as defects in 2d topologically twisted N=(2,2) theories) always come with complementary projection defects, and that the unprojected theory decomposes into the theories associated to the two projection defects. We demonstrate this in the context of Landau-Ginzburg orbifold theories.

arXiv commentv2: 16 pages, minor changes

References in corpus (9)

• Defect lines, dualities, and generalised orbifolds
• Orbifold completion of defect bicategories
• Defects and Bulk Perturbations of Boundary Landau-Ginzburg Orbifolds
• Adjunctions and defects in Landau-Ginzburg models
• B-type defects in Landau-Ginzburg models
• Orbifolds of n-dimensional defect TQFTs
• Undoing decomposition
• Realizing IR theories by projections in the UV
• Renormalization group defects for boundary flows

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