# Lattice field theory with torsion

## TL;DR

This paper explores lattice field theory incorporating torsion via dislocations, analyzing the chiral torsional effect through numerical and analytical methods, linking gravity and crystal defect duality.

## Contribution

It introduces a lattice model with torsion represented by dislocations and derives analytical formulas for the chiral torsional effect in the continuum limit.

## Key findings

- Numerical computation of vector and axial currents induced by dislocations.
- Analytical formula for the chiral torsional effect.
- Demonstration of the gravity-defect duality concept.

## 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.