The Einstein-like field theory and the renormalization of the shear modulus

The Einstein-like field theory is developed to describe elastic solid containing distribution of screw dislocations with finite-sized core. The core self-energy is given by the gauge-translational Lagrangian quadratic in the torsion tensor corresponding to three-dimensional Riemann–Cartan geometry. The Hilbert–Einstein gauge equation plays the role of unconventional incompatibility law. The stress tensor of the modified screw dislocations is smoothed out within the core. The renormalization of the shear modulus caused by proliferation of dipoles of non-singular screw dislocations is studied.