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Abstract
Inspired by the duality between gravity and defects in crystals, we study lattice field theory with torsion. The torsion is realized by a line defect of a lattice, namely a dislocation. As the first application, we perform the numerical computation for vector and axial currents induced by a screw dislocation. This current generation is called the chiral torsional effect. We also derive the analytical formula for the chiral torsional effect in the continuum limit.
Highlights
Quantum field theory in a curved space shows various intriguing phenomena
In solid-state physics, there is an interesting idea that gravitational effects can be mimicked by distorted lattices in crystals. (See textbooks [1,2] and references therein.) Since this emergent gravity is more controllable than genuine gravity, we will have a better chance for direct observation
Lattice defects behave as sources of the emergent gravity: a disclination corresponds to curvature, and a dislocation corresponds to torsion
Summary
Quantum field theory in a curved space shows various intriguing phenomena. we want to observe and confirm such gravity-induced phenomena, direct observation is not easy. Lattice defects behave as sources of the emergent gravity: a disclination corresponds to curvature, and a dislocation corresponds to torsion. There are many proposals to study gravity-induced phenomena through these lattice defects [3,4,5,6,7,8,9,10]. Introducing lattice defects to lattice field theory, we can simulate quantum field theory in a curved space. There are two motivations for this attempt This is a nonperturbative framework to study gravity-induced quantum phenomena. The new formulation allows us to simulate curvature and the torsion This is the exact calculation for the emergent gravity in solid-state physics.
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