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October 2007 Exotic statistics for strings in 4d BF theory
John C. Baez, Derek K. Wise, Alissa S. Crans
Adv. Theor. Math. Phys. 11(5): 707-749 (October 2007).


After a review of exotic statistics for point particles in 3d BF theory, and especially 3d quantum gravity, we show that string-like defects in 4d BF theory obey exotic statistics governed by the “loop braid group”. This group has a set of generators that switch two strings just as one would normally switch point particles, but also a set of generators that switch two strings by passing one through the other. The first set generates a copy of the symmetric group, while the second generates a copy of the braid group. Thanks to recent work of Xiao-Song Lin, we can give a presentation of the whole loop braid group, which turns out to be isomorphic to the “braid permutation group” of Fenn, Rimányi, and Rourke. In the context of 4d BF theory, this group naturally acts on the moduli space of flat $G$-bundles on the complement of a collection of unlinked unknotted circles in $\mathbb{R}^3$. When $G$ is unimodular, this gives a unitary representation of the loop braid group. We also discuss “quandle field theory”, in which the gauge group $G$ is replaced by a quandle.


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John C. Baez. Derek K. Wise. Alissa S. Crans. "Exotic statistics for strings in 4d BF theory." Adv. Theor. Math. Phys. 11 (5) 707 - 749, October 2007.


Published: October 2007
First available in Project Euclid: 13 December 2007

zbMATH: 1134.81039
MathSciNet: MR2362007

Rights: Copyright © 2007 International Press of Boston


Vol.11 • No. 5 • October 2007
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