@article{f03a73edf9ea420ea3179709842bf99b,

title = "Three-dimensional quantum gravity coupled to gauge fields",

abstract = "We show how to simulate U(1) gauge fields coupled to three-dimensional quantum gravity and then examine the phase diagram of this system. Quenched mean field theory suggests that a transition separates confined and deconfined phases (for the gauge matter) in both the negative curvature phase and the positive curvature phase of the quantum gravity, but numerical simulations find no evidence for such transitions.",

author = "Renken, {Ray L.} and Catterall, {Simon M.} and Kogut, {John B.}",

note = "Funding Information: where Nmax is the number of monopoles in the largest cluster and N~ is the total number of monopoles. M is a good order parameter for a percolation transition, a transition from a phase with many clusters to a phase with one cluster. In the three-dimensional quantum gravity plus U(1) gauge fields system, the monopole density is 1/3 when A = 0 and it slowly and smoothly decreases as A is increased. (On a cubic lattice the monopole density is 0.43 at A = 0 and decreases for larger A.) The density has very little sensitivity to the value of a. The cluster order parameter, M, is small for A = 0 and a in the region of the gravitational transition and it decreases smoothly as A is increased. Eventually it increases again, but this is only because the density becomes so small that there are of order unity monopoles (i.e. Nmax N~0~)M. also has no sensitivity to the value of a and this is surprising. In general, one expects a low percolation threshold for lattices with a high coordination number (such as those generated in the negative curvature phase). Apparently, it is the coordination number of the tetrahedron that counts (since that is where the monopole lives) rather than that of the sites. A tetrahedron has a coordination number of four, the same as a site in a two-dimensional square lattice, so one might guess that the threshold for the tetrahedral lattice is roughly that of the square lattice, namely 0.59 \[10\].This guess can be confirmed by artificially placing monopoles of a given density on the dynamical lattices and measuring the threshold directly. Consequently, the physical monopole density is always below the percolation threshold and they provide no useful signal. In conclusion, we have shown how to couple gauge fields to three-dimensional quantum gravity and made an effort to find an interesting continuum limit. Our discussion of detailed balance for gauge fields on a dynamical triangulation is new and can also be applied to four dimensions. We examined all of the possible options for obtaining a continuum theory of quantum gravity coupled to gauge fields. The gauge fields only weakly influenced the gravitational sector and had no effect on the order of that transition. No deconfinement transition, which also could have produced a continuum limit for this coupled system, was found either. Although disappointing, it is very useful to know that the obvious approach to coupling gauge fields and three-dimensional dynamical triangulations does not produce a viable theory. This work was supported, in part, by NSF grant PHY 92-00148. Some calculations were performed on the Florida State University Cray Y-MP, at the Pittsburgh Supercomputer Center, and on RS6000 IBM 550 RISC workstations at NCSA. We thank Olle Heinonen for discussions.",

year = "1994",

month = jul,

day = "11",

doi = "10.1016/0550-3213(94)90451-0",

language = "English (US)",

volume = "422",

pages = "677--689",

journal = "Nuclear Physics B",

issn = "0550-3213",

publisher = "Elsevier",

number = "3",

}