Yang-Mills Theory in Three Dimensions as Quantum Gravity Theory

Abstract

We perform the dual transformation of the Yang-Mills theory in d=3 dimensions using the Wilson action on the cubic lattice. The dual lattice is made of tetrahedra triangulating a 3-dimensional curved manifold but 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 colour space. The Yang-Mills theory can be identically rewritten as a quantum gravity theory with the Einstein-Hilbert action but purely imaginary Newton constant, plus a homogeneous `matter' term. Interestingly, the theory can be formulated in a gauge-invariant and local form without explicit colour degrees of freedom.

35 pages, 7 figures

Cited by in corpus (10)

• Dual Computations of Non-abelian Yang-Mills on the Lattice
• Gravitational Wilson Loop in Discrete Quantum Gravity
• One more variant of discrete gravity having "naive" continual limit
• A Dual Non-abelian Yang-Mills Amplitude in Four Dimensions
• Non-Abelian Stokes Theorems in Yang-Mills and Gravity Theories
• Analytic derivation of dual gluons and monopoles from SU(2) lattice Yang-Mills theory. II. Spin foam representation
• Plaquette representation for 3D lattice gauge models: I. Formulation and perturbation theory
• Howe Duality for an Induced Model of Lattice U(N) Yang-Mills Theory
• Dual representation of Polyakov loop in 3d SU(2) lattice Yang-Mills theory
• An exact string representation of 3d SU(2) lattice Yang--Mills theory