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.