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

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arxiv 2407.20333 v2 pith:A6H652EZ submitted 2024-07-29 hep-th math.AT

Christian Kneissl This is my paper · ORCID
classification hep-thmath.AT
keywords cobordismspinstringgroupsmathbbspectraltheorytype
verification ladder T0 review T1 audit T2 compute T3 formal

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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.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Non-supersymmetric branes and discrete topological terms

    hep-th 2025-07 conditional novelty 6.0 of 10

    A direct computation from the tentative NS5-brane spectrum gives the opposite Z3 topological term (1/3 vs 2/3) from Tachikawa-Zhang, so the spectrum or the inflow interpretation must change.

  2. Black $p$-Branes in Heterotic String Theory

    hep-th 2024-12 conditional novelty 6.0 of 10

    Numerical black brane solutions for the 0-brane and 4-brane of heterotic string theory are constructed, connecting linear-dilaton throats to asymptotically flat space, with the known 6-brane solution reproduced as a check.

  3. Cancelling mod-2 anomalies by Green-Schwarz mechanism with $B_{\mu\nu}$

    hep-th 2024-11 accept novelty 6.0 of 10

    Mod-2 global anomalies of 8d Sp(n) gauge theory can be canceled by a B-field Green-Schwarz mechanism, but the 4d SU(2) Witten anomaly cannot.

  4. Computations of Spin-Sp(4), Spin-SU(8), and Spin-Spin(16) bordism groups in dimensions up to 7

    math.AT 2025-04 reject novelty 4.0 of 10

    The Spin-Sp(4), Spin-SU(8), and Spin-Spin(16) bordism groups in dimensions up to 7 are stated with explicit generators, but the key Adams spectral sequence computation is omitted.

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