Remarks on mod-2 elliptic genus

2023/02/15 by Tachikawa, Yuji, Yamashita, Mayuko, Yonekura, Kazuya · 1 citation
#Algebraic Topology (math.AT) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th)

paper · doi:10.48550/arxiv.2302.07548

Abstract

For physicists: For supersymmetric quantum mechanics, there are cases when a mod-2 Witten index can be defined, even when a more ordinary ℤ-valued Witten index vanishes. Similarly, for 2d supersymmetric quantum field theories, there are cases when a mod-2 elliptic genus can be defined, even when a more ordinary elliptic genus vanishes. We study such mod-2 elliptic genera in the context of N=(0,1) supersymmetry, and show that they are characterized by mod-2 reductions of integral modular forms, under some assumptions. For mathematicians: We study the image of the standard homomorphism π_n TMF→ π_n KO((q))≃ ℤ/2((q)) for n=8k+1 or 8k+2, by relating them to the mod-2 reductions of integral modular forms.

Cited by

• On a long exact sequence of groups of equivalence classes of 2d N=(0,1) SQFTs

Related

• Mock modularity and a secondary elliptic genus
• Supersymmetric index on T² x S² and elliptic genus
• On invariants of two-dimensional minimally supersymmetric field theories
• On the Elliptic Genus and Mirror Symmetry
• A geometric construction of the Witten genus, II