1999/12/31 by Dmitri Diakonov, V. Petrov, Victor Petrov · 13 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Cosmology and Gravitation Theories #Gauge theory #Hořava–Lifshitz gravity #Mathematical physics #Noncommutative and Quantum Gravity Theories #Physics #Quantum #Quantum dynamics #Quantum field theory #Quantum gravity #Quantum mechanics #Quantum process #Theoretical physics #Yang–Mills theory #hep-lat #hep-th
paper · pdf · doi:10.1134/1.1334978
published in Journal of Experimental and Theoretical Physics 91(5), 873-893 (Pleiades Publishing) · 35 pages, 7 figures
arxiv created 2000/01/13 · openalex publication_date 2000/11/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We perform the dual transformation of theYang-Mills theory in three dimensions using the Wilson action on the cubic lattice. The dual lattice is made of tetrahedra triangulating a 3-dimensional curved manifold but which is embedded into a flat 6-dimensional space [for the SU(2) gauge group]. In the continuum limit, the theory can be reformulated in terms of 6-component gauge-invariant scalar fields having the meaning of the external coordinates of the dual lattice sites. These 6-component fields induce a metric and a curvature of the 3-dimensional dual-color space. The Yang-Mills theory can also be rewritten as a quantum gravity theory with the Einstein-Hilbert action but with a purely imaginary Newton constant plus a homogeneous “ether” term. The theory can be formulated in a gauge-invariant and local form without explicit color degrees of freedom.