  We construct deformation invariants of $2|1$-dimensional Euclidean field
theories valued in a cohomology theory approximating topological modular forms.
This implies several results anticipated by Stolz and Teichner and gives the
first torsion invariants of field theories valued in $\pi_*{\rm TMF}$. The
framework leads to a version of the elliptic Euler class described in terms of
field-theoretic data, as well as a partial construction of the supersymmetric
sigma model with target a string manifold.
