Year: 2026
Type: preprint
Abstract: In this paper, we study de Rham realizations for finite orientifold quotients. On the orientation preserving inertia of an almost complex global quotient we construct an anti-linear involution of the Chen-Hu algebra whose fixed subalgebra is a real form of the Chen-Ruan algebra. For genuine orientation reversing fixed sectors we prove that no coordinate invariant single sector fractional age exists. When a Calabi-Yau volume line is preserved, the relative phases define a canonical class $[μ_{\mathbb R}]\in H^2(\widehat G;\mathbb Z_ε)$. We identify this class with the Bockstein obstruction to a coherent real phase lift and prove that its vanishing is equivalent, after rephasing the volume form, to a phase trivial orientifold action. We then formulate a general Euler-Gysin realization theorem using relative Fredholm bundles and determinant-line sewing. For phase trivial Calabi-Yau surfaces we verify the admissibility conditions directly and obtain a canonically defined associative graded cohomology algebra containing the Chen-Hu even sector and the odd fixed surfaces. For an Eisenstein abelian surface with an order six dihedral action we compute the centralizer invariant algebra explicitly; it is a $16$ dimensional Frobenius algebra whose odd sector multiplication is noncommutative in the shifted grading. We also explain the relation with earlier unoriented orbifold cohomology constructions.
Source: arXiv (Cornell University)
Author: Li, Xiaobin
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G2946282769, G3589661357
OpenAlex ID: W7214088436