spin geometry, string geometry, fivebrane geometry …
rotation groups in low dimensions:
see also
Classical groups
Finite groups
Group schemes
Topological groups
Lie groups
Super-Lie groups
Higher groups
Cohomology and Extensions
Related concepts
∞-Lie theory (higher geometry)
Background
Smooth structure
Higher groupoids
Lie theory
∞-Lie groupoids
∞-Lie algebroids
Formal Lie groupoids
Cohomology
Homotopy
Related topics
Examples
$\infty$-Lie groupoids
$\infty$-Lie groups
$\infty$-Lie algebroids
$\infty$-Lie algebras
The semi-spin group in dimension 32.
In heterotic string theory precisely two (isomorphism classes of) gauge groups are consistent (give quantum anomaly cancellation): one is the direct product group $E_8 \times E_8$ of the exceptional Lie group E8 with itself, the other is in fact the semi-spin group $SemiSpin(32)$ (see McInnes 99a, p. 5).
Beware that the string theory literature often writes this as Spin(32)$/\mathbb{Z}_2$, which is at best ambiguous and misleading, or even as SO(32), which is wrong. Of course this follows the general tradition in the physics literature to write identifications of Lie groups that are really only identifications of their Lie algebras, see also “SO(10)-GUT theory”.
rotation groups in low dimensions:
see also
Brett McInnes, The Semispin Groups in String Theory, J. Math. Phys. 40:4699-4712, 1999 (arXiv:hep-th/9906059)
Brett McInnes, Gauge Spinors and String Duality, Nucl. Phys. B577:439-460, 2000 (arXiv:hep-th/9910100)
Last revised on May 15, 2019 at 15:41:38. See the history of this page for a list of all contributions to it.