| lt is conjectured that the tmf spectrum, constructed by Hopkins and Miller, can be described in terms of 'spaces' of conformal field theories. In this dissertation, spaces of field theories are constructed as classifying spaces of categories whose objects are certain types of field theories. These categories have symmetric monoidal structures and their sets of components turn out to form groups. Therefore; by work of Segal in the 70s, their classifying spaces are infinite loop spaces, hence define generalized cohomology theories. There are the following two examples. (i) A category SEFTn is constructed for each n ∈ Z whose objects are Stolz-Teichner's (1|1)-dimensional super Euclidean field theories of degree n. It is proved that the classifying space | SEFTn | represents the degree n K or KO cohomology. Whether we have K or KO depends on the coefficients of the field theories. (ii) There are (2|1)-dimensional field theories, called 'annular field theories', defined using supergeometric versions of circles and annuli only. Using these field theories as objects, a category AFTn is constructed for each n ∈ Z . It is proved that the classifying space | AFTn | represents the degree n elliptic cohomology associated with the Tate curve. Detailed definitions of the field theories are given. |
