Influence of the measure

4.7 Influence of the measure

The inclusion of a local measure term corresponding to $μ (det g)2$ was studied by Brügmann and Marinari [56 , 57 , 58 ]. This amounts to adding to the action a term of the form $∑ − μ lno(v)∕5 v$ , where $o(v)$ is the number of 4-simplices containing a vertex $v$ . For $μ = − 5,− 1,1,5$ , this seems to lead merely to a shift of the critical line. This setting has been revived recently by Renken [178

, 177

] in the context of a renormalization group analysis.