Gravity and Strings

4.6 Teleparallelism 149
this result. Checking that this is (or not) the case in the above family of theories requires an
expansion to order O(A 3 ) that would be interesting to do.
It is amusing to compare these results with the linearized limit of the low-energy string
effective action (see Chapter 15). The linearized actions are identical, except for the presence
of the dilaton in the string case. However, the non-linear actions are quite different: in
the string case, we simply have standard gravity coupled to matter (the Kalb–Ramond field)
that appears only quadratically (at least to lowest order in α ′ ), whereas, in the teleparallel
case, the Kalb–Ramond field should also appear non-linearly in the full action.
It is possible to view the theories of teleparallelism as gauge theories of the group of
translations [237, 521] with the Vielbeins playing the role of gauge vectors, but we will not
enter into this interesting aspect.