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We relate two classical dualities in low-dimensional quantum field theory: Kramers-Wannier duality of the Ising and related lattice models in $2$ dimensions, with electromagnetic duality for finite gauge theories in $3$ dimensions.
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Daniel S. Freed and Frank Quinn, Chern-Simons theory with finite gauge group , Comm. Math. Phys. 156
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Daniel S. Freed, Higher algebraic structures and quantization , Comm. Math. Phys. 159
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John C. Baez and James Dolan, Higher-dimensional algebra and topological quantum field theory , J. Math. Phys. 36
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E. Witten, On S S -duality in abelian gauge theory , Selecta Math. (N.S.) 1
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G. W. Moore and G. B. Segal, D-branes and K K -theory in 2D topological field theory , Dirichlet branes and mirror symmetry (Paul S. Aspinwall, Tom Bridgeland, Alastair Craw, Michael R. Douglas, Mark Gross, Anton Kapustin, Gregory W. Moore, Graeme Segal, Balázs Szendrői, and P. M. H. Wilson, eds.), Clay Mathematics Monographs, vol. 4, American Mathematical Society, Providence, RI, 2009, pp. x+681. arXiv:hep-th/0609042
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Pavol Severa, (Non-)Abelian Kramers-Wannier Duality And Topological Field Theory , Journal of High Energy Physics 2002
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2010
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Vladimir Turaev, Homotopy quantum field theory , EMS Tracts in Mathematics, vol. 10, European Mathematical Society (EMS), Zürich, 2010. Appendix 5 by Michael Müger and Appendices 6 and 7 by Alexis Virelizier
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O. Davidovich, State sums in 2 2 -dimensional fully extended topological field theories , Ph.D. thesis, University of Texas at Austin, 2011. http://repositories.lib.utexas.edu/handle/2152/ETD-UT-2011-05-3139
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Daniel S. Freed, The cobordism hypothesis , Bull. Amer. Math. Soc. (N.S.) 50
2013
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Daniel S. Freed and Constantin Teleman, Relative quantum field theory , Comm. Math. Phys. 326
2014
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2014
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Pavel Etingof, Shlomo Gelaki, Dmitri Nikshych, and Victor Ostrik, Tensor categories , Mathematical Surveys and Monographs, vol. 205, American Mathematical Society, Providence, RI, 2015
2015
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2015
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Constantin Teleman, Five lectures on topological field theory , Geometry and Quantization of Moduli Spaces, Springer, 2016, pp. 109–164. http://math.berkeley.edu/ ∼ \sim teleman/math/barclect.pdf
2016
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D. S. Freed, CBMS lectures , 2017. in preparation
2017
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