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

Abstract

Cobordism offers an 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.