String theory reduces to ordinary field theory in the infinite string tension limit. In this limit, the massive modes are decoupled and we are left with solely, the massless modes.

In fact, Bern and Kosower (Please, see a modern review by Christian Schubert. ) proved that the computation of the field theory amplitudes from the string amplitudes at the infinite string tension limit has many advantages:

The group theory and symmetry factors of the loops are all embedded in the string amplitude and thus are trivial. A string loop diagram includes a sum of many field theory loop diagrams. Gamma matrix manipulations are not needed in general. In addition, the integration over the string moduli space for multi-loop string amplitudes reduces to a sum over corners of the moduli space orbifold in the infinite tension limit. Also, the compactification of extra dimensions (in the appropriate string theory) adds only trivial factors to the field theory amplitude.

The main difficulty is that the string theory amplitudes are on-shell, but in certain cases it can be extended to an off-shell magnitude.

Referring to your specific question, the bosonic string is not the appropriate string theory for QED photon scattering amplitudes because it does not contain massless fermions in the spectrum. For (spinor) QED, one needs to consider an appropriate heterotic string as Bern and Kosower did in their article. When the appropriate theory is taken, the number of loops of the string amplitude is the same of the field theory number of loops in the infinite string tension limit.

However, from an open bosonic string theory, one can obtain pure gluon interactions and in fact, the gluonic beta function was obtained from this formalism even prior to Bern and Kosower work. (Of course, the QED beta function can also be obtained from the Heterotic theory).

It is important to mention that the string magnitudes are consistent only when the conformal symmetry is maintained. Thus, in this formalism, masses are obtained from infrared regularization.

This post imported from StackExchange Physics at 2014-04-13 14:41 (UCT), posted by SE-user David Bar Moshe