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An invertible (extended) functorial field theory is one which is an invertible object under the tensor product on TQFTs [Freed & Moore (2006), Def. 5.7], which essentially means that it is one whose target category is a rigid symmetric monoidal groupoid, a Picard groupoid (DGP 19, p.20).
The proposal to understand quantum anomalies of lower-dimensional non-invertible (and possibly non-topological) quantum field theories as invertible topoligical field theories:
Daniel S. Freed, Gregory W. Moore, Def. 5.7 in: Setting the quantum integrand of M-theory, Commun. Math. Phys. 263 (2006) 89-132 [arXiv:hep-th/0409135, doi:10.1007/s00220-005-1482-7]
Daniel S. Freed, Michael J. Hopkins, Constantin Teleman, very last sentence of: Consistent Orientation of Moduli Spaces [arXiv:0711.1909]
Daniel Freed, Anomalies and Invertible Field Theories, talk at StringMath2013, Proc. Symp. Pure Math, Proc. Sympos. Pure Math. 88, Amer. Math. Soc. (2014) 25–45 [arXiv.1404.7224]
Daniel S. Freed: What is an anomaly?, talk at Mathematical Picture Language Seminar, Feb 2023 [arXiv:2307.08147, video:YT, slides:pdf]
As formalizing short-range entanglement in topological phases of matter:
On classification (via reflection positivity):
Review:
Relation to cutting and pasting of manifolds:
Carmen Rovi, Matthew Schoenbauer, Relating Cut and Paste Invariants and TQFTs, The Quarterly Journal of Mathematics 73 2 (2022) 579–607 [arXiv:1803.02939, doi:10.1093/qmath/haab044]
Carmen Rovi, Relating cut and paste invariants and TQFTS, talk at CQTS (Apr. 2023) [video: YT]
Mayuko Yamashita, Invertible QFTs and differential Anderson duals [arXiv:2304.08833]
Application to anomalies of gapped systems:
Gapped theories have torsion anomalies [arXiv:2408.15148]
Last revised on August 28, 2024 at 05:03:02. See the history of this page for a list of all contributions to it.