On extended TQFTs modelling topological phases of matter in solid state physics:
Suggestion that the Chern-Dold character from tmf to modular forms, sends a 2d SCFT to its partition function/elliptic genus/supersymmetric index:
and discussion of the 2d SCFTs (namely supersymmetric SU(2)-WZW-models) conjecturally corresponding, under this conjectural identification, to the elements of $\mathbb{Z}/24$ $\simeq$ $tmf^{-3}(\ast) = \pi_3(tmf)$ $\simeq$ $\pi_3(\mathbb{S})$ (the third stable homotopy group of spheres):
Davide Gaiotto, Theo Johnson-Freyd, Edward Witten, p. 17 of: A Note On Some Minimally Supersymmetric Models In Two Dimensions, (arXiv:1902.10249) in S. Novikov et al. Integrability, Quantization, and Geometry: II. Quantum Theories and Algebraic Geometry, Proc. Symposia Pure Math., 103(2), 2021 (ISBN: 978-1-4704-5592-7)
Davide Gaiotto, Theo Johnson-Freyd, Mock modularity and a secondary elliptic genus (arXiv:1904.05788)
Theo Johnson-Freyd, Topological Mathieu Moonshine (arXiv:2006.02922)
On Lie groups and quantum groups:
Last revised on September 20, 2021 at 12:54:27. See the history of this page for a list of all contributions to it.