Spin cobordism and the gauge group of type I/heterotic string theory

TL;DR

This paper computes the spin cobordism groups related to type I/heterotic string theory using algebraic topology tools, revealing non-perturbative sectors and global symmetry constraints crucial for quantum gravity consistency.

Contribution

It provides the first detailed computation of spin cobordism groups for the classifying space of $Spin(32)/Z_2$, connecting algebraic topology with string theory non-perturbative aspects.

Findings

Computed spin cobordism groups relevant to type I/heterotic string theory.

Linked cobordism groups to non-perturbative string theory sectors.

Provided a string theoretic interpretation of the cobordism results.

Abstract

Cobordism offers a unique perspective into the non-perturbative sector of string theory by demanding the absence of higher form global symmetries for quantum gravitational consistency. In this work we compute the spin cobordism groups of the classifying space of $Spin(32)/\mathbb{Z}_2$ relevant to describing type I/heterotic string theory and explore their (shared) non-perturbative sector. To facilitate this we leverage our knowledge of type I D-brane physics behind the related ko-homology. The computation utilizes several established tools from algebraic topology, the focus here is on two spectral sequences. First, the Eilenberg-Moore spectral sequence is used to obtain the cohomology of the classifying space of the $Spin(32)/\mathbb{Z}_2$ with $\mathbb{Z}_2$ coefficients. This will enable us to start the Adams spectral sequence for finally obtaining our result, the spin cobordism groups. We conclude by providing a string theoretic interpretation to the cobordism groups.