The field-theoretic model conjecture for periodic topological modular forms

The paper considers $2|1$-dimensional Euclidean field theories, whose partition functions are modular functions, and writes $2|1\text{-}\operatorname{EFT}^n_{loc}[X]$ for the degree-$n$ local field theories over a space $X$. The theory $\operatorname{TMF}^*$ denotes the periodic cohomology theory of topological modular forms, with periodicity $24^2$. The field-theoretic model conjecture. There is an isomorphism

$$2|1\text{-}\operatorname{EFT}^n_{loc}[X]\cong \operatorname{TMF}^n(X)$$

compatible with the multiplicative structure. The periodicity class has modular form the 24th power of the discriminant, and the 48-periodicity of the field-theoretic model is expected to become $24^2$-periodicity after incorporating locality. This proposes local $2|1$-dimensional Euclidean field theories as a geometric model for periodic topological modular forms; the source presents the identification as an expectation rather than an established theorem.