### 4.8 Higher-derivative terms

Higher-order derivative terms were considered by Ambjørn et al. [16] (see also [143]), who added a term
of the form
to the action, where again and denotes the number of 4-simplices sharing a bone .
For , and with volumes up to , no major qualitative changes of the geometrical
observables were found. The inclusion of the higher-derivative term also does not improve the behaviour of
the average curvature , which continues to be positive at the critical point, whereas from a
naïve comparison with the continuum theory one would expect it to scale to zero. (This is
also incompatible with the prediction of Antoniadis et al [20], should dynamical triangulations
possess an infrared stable fixed point.) De Bakker and Smit [89] have argued that this may
not be a reason of concern, since one expects the volume and curvature terms to mix under
renormalization.