The construction of Dirac operators on orientifolds

JOURNAL OF GEOMETRY AND PHYSICS

卷:170

Article

Kitson, Simon¹ 

[1] Australian Natl Univ, Canberra, ACT, Australia

关键词: Orientifold;    Anti-linearity;    KR-theory;    Dirac operator;    K-homology;    Wigner's theorem;   

DOI  :  10.1016/j.geomphys.2021.104361

来源: Elsevier

【 摘 要 】

Motivated by Wigner's theorem, a canonical construction is described that produces an Atiyah-Singer Dirac operator with both unitary and anti-unitary symmetries. This Dirac operator includes the Dirac operator for KR-theory as a special case, filling a long-standing gap in the literature. In order to make the construction, orientifold Spin(c)-structures are defined and classified using semi-equivariant Dixmier-Douady theory, and analogues of several standard theorems on the existence of Spine-structures are proved. (C) 2021 Elsevier B.V. All rights reserved.

【 授权许可】

Free