  The field theory of a short range spin glass with Gaussian random
interactions, is considered near the upper critical dimension six. In the
glassy phase, replica symmetry breaking is accompanied with massless Goldstone
modes, generated by the breaking of reparametrization invariance of a Parisi
type solution. Twisted boundary conditions are thus imposed at two opposite
ends of the system in order to study the size dependence of the twist free
energy. A loop-expansion is performed to first order around a twisted
background. It is found, as expected but it is non trivial, that the theory
does renormalize around such backgrounds, as well as for the bulk. However two
main differences appear, in comparison with simple ferromagnetic transitions :
(i) the loop expansion yields a (negative) anomaly in the size dependence of
the free energy, thereby lifting the lower critical dimension to a value
greater than two given by $d_c = 2-\eta(d_c)$ (ii) the free energy is lowered
by twisting the boundary conditions. This sign may reflect a spontaneous
spatial non-uniformity of the order parameter.
