nLab string geometry

Contents

Ingredients

Dynkin label	sp. orth. group	spin group	pin group	semi-spin group
	SO(2)	Spin(2)	Pin(2)
B1	SO(3)	Spin(3)	Pin(3)
D2	SO(4)	Spin(4)	Pin(4)
B2	SO(5)	Spin(5)	Pin(5)
D3	SO(6)	Spin(6)
B3	SO(7)	Spin(7)
D4	SO(8)	Spin(8)		SO(8)
B4	SO(9)	Spin(9)
D5	SO(10)	Spin(10)
B5	SO(11)	Spin(11)
D6	SO(12)	Spin(12)
	$\vdots$	$\vdots$
D8	SO(16)	Spin(16)		SemiSpin(16)
	$\vdots$	$\vdots$
D16	SO(32)	Spin(32)		SemiSpin(32)

The analog of spin geometry as one passes from spinning particles to spinning strings. To some extent the step from the spin group to the string 2-group.

detailed discussion of the relation to spin geometry in smooth loop spaces is in

Konrad Waldorf, String geometry vs. spin geometry on loop spaces (arXiv:1403.5656)

related remarks are briefly in

Chris Kottke with Richard Melrose, A very smooth Dirac operator on loop space (pdf)

Last revised on April 24, 2017 at 09:34:18. See the history of this page for a list of all contributions to it.