Chromatic homotopy theory is a subfield of stable homotopy theory that studies complex-oriented cohomology theories from the "chromatic" point of view, which is based on Quillen's work relating cohomology theories to formal groups. In this picture, theories are classified in terms of their "chromatic levels"; i.e., the heights of the formal groups that define the theories via the Landweber exact functor theorem. Typical theories it studies include: complex K-theory, elliptic cohomology, Morava K-theory and tmf.
While:
K-theory is useful to study (1) the D-branes in string theory, (2) Fermi surfaces and their low energy excitations, (3) classifications of topological insulators and superconductors.
tmf is also related to supersymmetric field theory. Say tmf(𝑛) is the space of supersymmetric conformal field theories of central charge −𝑛: https://physics.stackexchange.com/questions/26853/tmfn-is-the-space-of-supersymmetric-conformal-field-theories-of-central-charge
My question: Has the chromatic homotopy theory, a subfield of stable homotopy theory that studies complex-oriented cohomology theories from the "chromatic" point of view, been found its application in physics? Which fields in physics? What are the relations then?
