Abstract
We develop a new description of curved manifolds that represent a topological phase for the usual Levi-Civita connection and a dynamical phase for the torsion, being the only part of the connection that generates curvature. The holonomy group structure of such manifolds is studied, and different expressions of the torsion in terms of gauge fields are considered with the purpose to describe different dynamical scenarios. Additionally some models of torsion interacting with fermions are constructed; specifically a four-dimensional model that mimics an usual fermion-gauge fields system is considered; this model undergoes parity symmetry breaking with a dynamical background. Since these manifolds represent new gravitational backgrounds, we speculate on possible applications in the study of qualitative and quantitative aspects of the gauge/gravity duality.
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