Higher-derivative terms

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 $c4 = 4.767$ and $o(b)$ denotes the number of 4-simplices sharing a bone $b$ . For $h ∈ [0,20]$ , and with volumes up to $32k$ , 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 $⟨R ⟩$ , 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.