4.10 Non-spherical lattices4 Dynamical triangulations4.8 Higher-derivative terms

4.9 Coupling to matter fields

Ambjørn et al [7] considered the influence of both Ising spins and Gaussian scalar fields on bulk geometric quantities. The phase structure remained essentially unchanged, and no improvement in the scaling behaviour of tex2html_wrap_inline2489 was found. Taken together with their results on higher-derivative gravity [16Jump To The Next Citation Point In The Article], one finds a universal linear dependence of the cosmological constant tex2html_wrap_inline2967, with slope tex2html_wrap_inline3045 .

Coupling to tex2html_wrap_inline2739 -spin variables s (l) located on edges l was considered by Ambjørn et al [15], who added a Wilson loop term tex2html_wrap_inline3053 to the action. The matter sector behaves largely as expected when tex2html_wrap_inline2917 is varied between the crumpled and the elongated gravity phase. However, in the common critical region of both sectors, where a priori one might have expected interesting effects, the critical behaviour seems to agree with that of the pure gravity system.

More recently, Bilke et al [52] have reported a non-trivial back-reaction of matter on geometry, when considering coupling to several non-compact U (1)-gauge fields. Their study was in part motivated by a continuum analysis of the dynamics of the conformal factor of Antoniadis et al [21]. Including three fields U (1)-fields seems to lead to a total suppression of the branched polymer phase, which is replaced by a new weak-coupling phase with negative susceptibility exponent tex2html_wrap_inline2959 and a fractal dimension tex2html_wrap_inline3063 . These are clearly interesting results, but should be treated with some caution because of the small lattice sizes involved (tex2html_wrap_inline3065).



4.10 Non-spherical lattices4 Dynamical triangulations4.8 Higher-derivative terms

image Discrete Approaches to Quantum Gravity in Four Dimensions
Renate Loll
http://www.livingreviews.org/lrr-1998-13
© Max-Planck-Gesellschaft. ISSN 1433-8351
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