A spin foam model for pure gauge theory coupled to quantum gravity

Abstract

We propose a spin foam model for pure gauge fields coupled to Riemannian quantum gravity in four dimensions. The model is formulated for the triangulation of a four-manifold which is given merely combinatorially. The Riemannian Barrett--Crane model provides the gravity sector of our model and dynamically assigns geometric data to the given combinatorial triangulation. The gauge theory sector is a lattice gauge theory living on the same triangulation and obtains from the gravity sector the geometric information which is required to calculate the Yang--Mills action. The model is designed so that one obtains a continuum approximation of the gauge theory sector at an effective level, similarly to the continuum limit of lattice gauge theory, when the typical length scale of gravity is much smaller than the Yang--Mills scale.

18 pages, LaTeX, 1 figure, v2: details clarified, references added

References in corpus (11)

• Spacetime geometry from algebra: spin foam models for non-perturbative quantum gravity
• Geometrical measurements in three-dimensional quantum gravity
• Spin Foam Models of Riemannian Quantum Gravity
• Barrett-Crane spin foam model from generalized BF-type action for gravity
• Spin Foam Models of Matter Coupled to Gravity
• Positivity of Spin Foam Amplitudes
• Boundary terms in the Barrett-Crane spin foam model and consistent gluing
• Dual variables and a connection picture for the Euclidean Barrett-Crane model
• A New Approach to the Geometrization of Matter
• Exact duality transformations for sigma models and gauge theories
• The dual of non-Abelian Lattice Gauge Theory

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