4.8 Higher-derivative terms

Higher-order derivative terms were considered by Ambjørn et al. [16Jump To The Next Citation Point] (see also [143]), who added a term of the form
∑ ( )2 h c−2 o(b) c4 −-o(b) (23 ) 4 o(b) b
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.
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