Counting initial conditions and degrees of freedom in nonlocal gravity

Nonlocal quantum gravity is a class of fundamental theories whose classical and quantum dynamics is specified by "form factors", operators with infinitely many derivatives. After briefly reviewing this paradigm and its role in the resolution of big-bang and black-hole singularities, we count the number of nonpertubative field degrees of freedom as well as the number of initial conditions to be specified to solve the Cauchy problem. In particular, in four dimensions and for the string- related form factor, there are 8 degrees of freedom (2 graviton polarization modes, which propagate, and 6 nonpropagating rank-2 tensor modes) and 4 initial conditions. The method to obtain this result is illustrated for the case of a nonlocal scalar field.