Spectral asymmetry and supersymmetry
  Fractional charges, and in particular the spectral asymmetry eta of certain Dirac operators, can appear in the central charge of supersymmetric field theories. This yields unexpected analyticity constraints on eta from which classic results can be recovered in an elegant way. The method could also be applied in the context of string theory. 
Frank Ferrari (University of Neuchatel and Ecole Normale Superieure)