3.11 Coupling to scalar matter3 Quantum Regge Calculus3.9 Non-hypercubic lattices

3.10 Coupling to SU(2)-gauge fields

Berg and collaborators [42Jump To The Next Citation Point In The Article, 43Jump To The Next Citation Point In The Article, 44Jump To The Next Citation Point In The Article, 27Jump To The Next Citation Point In The Article, 28Jump To The Next Citation Point In The Article, 41Jump To The Next Citation Point In The Article] coupled the pure-curvature action geometrically to the Wilson action for SU(2)-gauge fields via dimensionless weight factors tex2html_wrap_inline2747,

  equation520

where tex2html_wrap_inline2749 denotes the SU(2)-holonomy around b and tex2html_wrap_inline2753 is proportional to the inverse square coupling constant, tex2html_wrap_inline2755 . One motivation was to understand whether in the well-defined pure-gravity region, one can choose the elementary particle masses to be tex2html_wrap_inline2757 as tex2html_wrap_inline2759, as one might expect for a realistic gravity+matter system. This seems a rather distant hope, since in the simulations performed so far, the ratio tex2html_wrap_inline2761 is of order unity.

Initial computations were performed on a tex2html_wrap_inline2763 -lattice with the scale-invariant measure, and at k =0.01 [42, 44], and extended to larger k -values in [43]. For tex2html_wrap_inline2769, one finds some evidence for a (first-order?) transition; the region of tex2html_wrap_inline2753 where the transition occurs does not change much with k . Beirl et al [27, 28] extended this analysis by measuring the static potential V of a quark-antiquark pair on lattices of size tex2html_wrap_inline2777 and tex2html_wrap_inline2779 . With and without gravity, one finds both a confined and a deconfined phase; in the presence of gravity, the transition occurs at a smaller tex2html_wrap_inline2753 -value. More recently, Berg et al [41] have gathered further data on the location and stability of the well-defined phase in the tex2html_wrap_inline2783 -plane, and extracted a string tension for various tex2html_wrap_inline2753 -values.



3.11 Coupling to scalar matter3 Quantum Regge Calculus3.9 Non-hypercubic lattices

image Discrete Approaches to Quantum Gravity in Four Dimensions
Renate Loll
http://www.livingreviews.org/lrr-1998-13
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