a talk that I have given:
Urs Schreiber$\;$ on joint work with $\;$ Hisham Sati
(Center for Quantum and Topological Systems, NYU Abu Dhabi)
TED K-theory of Cohomotopy moduli spaces and Anyonic Topological Order
at: Higher Structures and Field Theory
ESI, Vienna
download:
slides pdf (view on full screen)
Abstract: It is largely folklore that:
- 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;
- 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
but:
- full TED K-theory has never quite been formulated before;
- its M-theoretic/strongly-interacting enhancement has remained elusive.
This talk surveys:
our construction of full TED K-theory via cohesive $\infty$-topos theory;
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;
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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