On the possibility of large axion decay constants

The decay constant of the QCD axion is required by observation to be small compared with the Planck scale. In theories of 'natural inflation' and certain proposed anthropic solutions of the cosmological constant problem it would be interesting to obtain a large decay constant for axion-like fields from microscopic physics. String theory is the only context in which one can sensibly address this question. Here we survey a number of periodic fields in string theory in a variety of string vacua. In some examples, the decay constant can be parametrically larger than the Planck scale but the effective action then contains appreciable harmonics of order f(A)/M-p. As a result, these fields are no better inflaton candidates than Planck scale axions.