Schreiber TED K-theory of Cohomotopy moduli spaces and Anyonic Topological Order

a talk that I have given:

Abstract: It is largely folklore that:

  1. topological K-theory in its full twisted & equivariant & differential (TED) refinement classifies stable D-branes in string theory, as well as non-interacting topological insulator phases in condensed matter theory;
  2. some non-perturbative/strongly-interacting enhancement of this classification is needed to account for M-branes in string theory as well as for interacting topological order in condensed matter theory


  1. full TED K-theory has never quite been formulated before;
  2. its M-theoretic/strongly-interacting enhancement has remained elusive.

This talk surveys:

  1. our construction of full TED K-theory via cohesive \infty -topos theory;

  2. our Hypothesis H about its M-theoretic/strongly-interacting enhancement:

    instead of applying TED-K to the spacetime orbifold/Brillouin torus directly, it needs to be applied to the corresponding twisted Cohomotopy moduli space;

  3. how the resulting theory explains the nature of defect branes (such as D7-branes and “M3-branes”) in M-/F-theory as well as anyonic topological order in condensed matter theory.

This is a joint project with Hisham Sati

(e.g. arXiv:2203.11838, arXiv:2206.13563, and arXiv:2008.01101, arXiv:2112.13654).

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Last revised on August 26, 2022 at 13:18:12. See the history of this page for a list of all contributions to it.