We describe the role conformal nets, a mathematical model for conformal
field theory, could play in a geometric definition of the generalized
cohomology theory TMF of topological modular forms. Inspired by work
of Segal and Stolz-Teichner, we speculate that bundles of boundary
conditions for the net of free fermions will be the basic underlying
objects representing TMF-cohomology classes. String structures, which
are the fundamental orientations for TMF-cohomology, can be encoded
by defects between free fermions, and we construct the bundle of
fermionic boundary conditions for the TMF-Euler class of a string
vector bundle. We conjecture that the free fermion net exhibits an
algebraic periodicity corresponding to the 576-fold cohomological
periodicity of TMF; using a homotopy-theoretic invariant of invertible
conformal nets, we establish a lower bound of 24 on this periodicity
of the free fermions.
%0 Journal Article
%1 DouglasHenriques2011
%A Douglas, C. L.
%A Henriques, A. G.
%D 2011
%J ArXiv e-prints
%K - 55N34, 81T05 81T40, Algebraic Algebras, Energy High Mathematical Mathematics Operator Physics Physics, Theory, Topology,
%T Topological modular forms and conformal nets
%X We describe the role conformal nets, a mathematical model for conformal
field theory, could play in a geometric definition of the generalized
cohomology theory TMF of topological modular forms. Inspired by work
of Segal and Stolz-Teichner, we speculate that bundles of boundary
conditions for the net of free fermions will be the basic underlying
objects representing TMF-cohomology classes. String structures, which
are the fundamental orientations for TMF-cohomology, can be encoded
by defects between free fermions, and we construct the bundle of
fermionic boundary conditions for the TMF-Euler class of a string
vector bundle. We conjecture that the free fermion net exhibits an
algebraic periodicity corresponding to the 576-fold cohomological
periodicity of TMF; using a homotopy-theoretic invariant of invertible
conformal nets, we establish a lower bound of 24 on this periodicity
of the free fermions.
@article{DouglasHenriques2011,
abstract = {We describe the role conformal nets, a mathematical model for conformal
field theory, could play in a geometric definition of the generalized
cohomology theory TMF of topological modular forms. Inspired by work
of Segal and Stolz-Teichner, we speculate that bundles of boundary
conditions for the net of free fermions will be the basic underlying
objects representing TMF-cohomology classes. String structures, which
are the fundamental orientations for TMF-cohomology, can be encoded
by defects between free fermions, and we construct the bundle of
fermionic boundary conditions for the TMF-Euler class of a string
vector bundle. We conjecture that the free fermion net exhibits an
algebraic periodicity corresponding to the 576-fold cohomological
periodicity of TMF; using a homotopy-theoretic invariant of invertible
conformal nets, we establish a lower bound of 24 on this periodicity
of the free fermions.},
added-at = {2012-11-06T21:57:21.000+0100},
adsnote = {Provided by the SAO/NASA Astrophysics Data System},
adsurl = {http://adsabs.harvard.edu/abs/2011arXiv1103.4187D},
archiveprefix = {arXiv},
author = {{Douglas}, C. L. and {Henriques}, A. G.},
biburl = {https://www.bibsonomy.org/bibtex/2e0adb71c3003f133bf9bbde37d211703/jdthomas},
eprint = {1103.4187},
file = {DouglasHenriques2011.pdf:DouglasHenriques2011.pdf:PDF},
interhash = {02f162b69a2e5a387d883aad20b78c89},
intrahash = {e0adb71c3003f133bf9bbde37d211703},
journal = {ArXiv e-prints},
keywords = {- 55N34, 81T05 81T40, Algebraic Algebras, Energy High Mathematical Mathematics Operator Physics Physics, Theory, Topology,},
month = mar,
primaryclass = {math.AT},
timestamp = {2012-11-06T21:57:22.000+0100},
title = {{Topological modular forms and conformal nets}},
year = 2011
}