Fetching the paper…

Reading the bibliography…

2019

Conformal nets V: dualizability

Bartels, Arthur, Douglas, Christopher L., Henriques, André

Original
PDF
Post on X

Understand

We prove that finite-index conformal nets are fully dualizable objects in the 3-category of conformal nets.

Therefore, assuming the cobordism hypothesis applies, there exists a local framed topological field theory whose value on the point is any finite-index conformal net.
Along the way, we prove a Peter-Weyl theorem for defects between conformal nets, namely that the annular sector of a finite defect is the sum of every sector tensor its dual.

Conformal nets V: dualizability · Around

Built on

John C. Baez and James Dolan, Higher-dimensional algebra and topological quantum field theory , J. Math. Phys. 36
1995
Earlier work this paper cites.
Bojko Bakalov and Alexander Kirillov, Jr., Lectures on tensor categories and modular functors , University Lecture Series, vol. 21, American Mathematical Society, Providence, RI, 2001. MR 1797619 (2002d:18003)
2001
Earlier work this paper cites.
Yasuyuki Kawahigashi, Roberto Longo, and Michael Müger, Multi-interval subfactors and modularity of representations in conformal field theory , Comm. Math. Phys. 219
2001
Earlier work this paper cites.
Roberto Longo and Feng Xu, Topological sectors and a dichotomy in conformal field theory , Comm. Math. Phys. 251
2004
Earlier work this paper cites.
Jacob Lurie, On the classification of topological field theories , Current developments in mathematics, 2008, Int. Press, Somerville, MA, 2009, pp. 129–280. MR 2555928 (2010k:57064)
2009
Earlier work this paper cites.
by same author, Lecture notes on von Neumann algebras , 2011, http://www.math.harvard. edu/ ∼ \scriptstyle\sim lurie/261y.html
2011
Earlier work this paper cites.

Similar

Arthur Bartels, Christopher L. Douglas, and André Henriques, Dualizability and index of subfactors , Quantum Topology 5
Original
2014
Cited alongside, same era.
by same author, Conformal nets I: Coordinate-free nets , Int. Math. Res. Not. 13
Original
2015
Cited alongside, same era.
Damien Calaque and Claudia Scheimbauer, A note on the ( ∞ , n ) (\infty,n) -category of cobordisms , arXiv:1509.08906, 2015
Original
2015
Cited alongside, same era.
David Ayala and John Francis, The cobordism hypothesis , arXiv:1705.02240, 2017
Original
2017
Cited alongside, same era.
by same author, Conformal nets II: Conformal blocks , Comm. Math. Phys. 354
Original

Then

Christopher L. Douglas, Christopher Schommer-Pries, and Noah Snyder, Dualizable tensor categories , Mem. Amer. Math. Soc. (2017), arxiv:1312.7188
Original
2017
Later among the works it cites.
André Henriques, What Chern–Simons theory assigns to a point , Proc. Natl. Acad. Sci. USA 114
2017
Later among the works it cites.
by same author, g
Original
2018
Later among the works it cites.
Bin Gui, Categorical extensions of conformal nets , arXiv:1812.04470, 2018
Original
2018
Later among the works it cites.
by same author, Fusion of defects (formerly “Conformal nets III: Fusion of defects”) , Mem. Amer. Math. Soc. 1237
Original
2019

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

2017

Cited alongside, same era.

Closest in time.