Twisted String Bordism with Applications to Anomaly Cancellation
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Author(s)
Pacheco-Tallaj, Natalia María
Advisor(s)
Hopkins, Michael J.
Date Issued
May 2026
Publisher
Massachusetts Institute of Technology
Abstract
We study anomaly cancellation for six-dimensional N = (1, 0) supergravity with simply laced gauge group via the Dai-Freed formalism. When the Green–Schwarz mechanism is present, full anomaly cancellation reduces to the vanishing of a bordism invariant—a homomorphism out of a seven-dimensional twisted String bordism group. We compute these groups for type ADE gauge groups. In addition to the usual spectral sequence techniques, we also leverage a variety of geometric techniques such as Smith homomorphisms, and we use an unstable classification of vector bundles over ℂℙ² to construct explicit generators arising as 𝑆³ bundles over ℂℙ². We then construct a large family of bordism invariants—twisted analogs of the Adams 𝑒-invariant— detecting the torsion order of these generators. This is joint work with I. Basile, C. Krulewski, and G. Leone.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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