Type IIA String Theory and tmf with Level Structure

2024/11/11 by Debray, Arun, Yu, Matthew
#55P42 #55P43 #Algebraic Topology (math.AT) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2411.07299

Abstract

We look at a new string^h tangential structure first introduced by Devalapurkar and relate it to the W₇=0 condition of Diaconescu-Moore-Witten for type IIA string theory and M-theory. We show that a string^h structure on the target space automatically satisfies the W₇=0 condition and we also explain when the W₇=0 condition gives rise to a string^h structure. Devalapurkar initially constructed MString^h in such a way that it orients tmf₁(3), we extend Devalapurkar's orientation and show that MString^h orients tmf₁(n). We compute the homotopy groups of MString^h in the dimensions relevant for physical applications, and apply them to anomaly cancellation applications for compactifications of type IIA string theory.

Related

• M-Theory and String-String Duality
• M Theory, Type IIA Superstrings, and Elliptic Cohomology
• Fine-tuning problems in type IIA string theory
• M-Theory and Topological Strings--I
• Geometrical Structures of M-Theory