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

Urs Schreiber (NYU, Abu Dhabi)

Aug 25. 2022, 10:00 — 11:00

It is largely folklore that:

(a) 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; 

(b) 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:

(a) full TED K-theory has never quite been formulated before

(b) its M-theoretic/strong-interacting enhancement has remained elusive.

This talk surveys:

(a) our construction of full TED K-theory via cohesive infinity-topos theory;

(b) our "Hypothesis H" about its M-theoretic/strongly-interacting enhancement: instead of applying TED-K to the spacetime/Brillouin-torus directly, it needs to be applied to the corresponding twisted Cohomotopy moduli space.

(c) how the resulting theory explains the nature of defect branes (such as D7-branes) in M/F-theory as well as anyonic topological order (for su(2)-anyons) 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).

For talk slides and further pointers see: ncatlab.org/schreiber/show/TED-K+of+Cohomotopy+and+Anyons

Further Information
ESI Boltzmann Lecture Hall
Associated Event:
Higher Structures and Field Theory (Thematic Programme)
Anton Alekseev (U Genève)
Stefan Fredenhagen (U of Vienna)
Nicolai Reshetikhin (UC, Berkeley)
Thomas Strobl (U Lyon)
Chenchang Zhu (U Göttingen)