%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 }