Abstract
As put forward in [1] 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 \( \mathcal{N} \) = (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.
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References
F. Klos and D. Roggenkamp, Realizing IR theories by projections in the UV, JHEP 01 (2020) 097 [arXiv:1907.12339] [INSPIRE].
J. Fröhlich, J. Fuchs, I. Runkel and C. Schweigert, Defect lines, dualities, and generalised orbifolds, in 16th International Congress on Mathematical Physics, (2009), DOI [arXiv:0909.5013] [INSPIRE].
I. Brunner and D. Roggenkamp, Defects and bulk perturbations of boundary Landau-Ginzburg orbifolds, JHEP 04 (2008) 001 [arXiv:0712.0188] [INSPIRE].
D. Orlov, Triangulated categories of singularities and D-branes in Landau-Ginzburg models, Trudy Steklov Mat. Inst. 246 (2004) 240 [math/0302304] [INSPIRE].
A. Konechny, Renormalization group defects for boundary flows, J. Phys. A 46 (2013) 145401 [arXiv:1211.3665] [INSPIRE].
N. Carqueville, I. Runkel and G. Schaumann, Orbifolds of n-dimensional defect TQFTs, Geom. Topol. 23 (2019) 781 [arXiv:1705.06085] [INSPIRE].
I. Brunner and D. Roggenkamp, B-type defects in Landau-Ginzburg models, JHEP 08 (2007) 093 [arXiv:0707.0922] [INSPIRE].
N. Carqueville and D. Murfet, Adjunctions and defects in Landau-Ginzburg models, Adv. Math. 289 (2016) 480 [arXiv:1208.1481] [INSPIRE].
N. Carqueville and I. Runkel, Orbifold completion of defect bicategories, Quantum Topol. 7 (2016) 203 [arXiv:1210.6363] [INSPIRE].
E. Sharpe, Undoing decomposition, Int. J. Mod. Phys. A 34 (2020) 1950233 [arXiv:1911.05080] [INSPIRE].
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ArXiv ePrint: 2006.08961
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Klos, F., Roggenkamp, D. Complementary projection defects and decomposition. J. High Energ. Phys. 2021, 195 (2021). https://doi.org/10.1007/JHEP03(2021)195
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DOI: https://doi.org/10.1007/JHEP03(2021)195