# Duality Between Dirac Fermions in Curved Spacetime and Optical solitons in Non-Linear Schrodinger Model: Magic of $1+1$-Dimensional Bosonization

## TL;DR

This paper explores the duality between Dirac fermions in curved spacetime and optical solitons in a non-linear Schrödinger model, revealing how bosonization links these phenomena in 1+1 dimensions and connecting fermionic and solitonic solutions.

## Contribution

It demonstrates the mapping of Dirac fermions in curved spacetime to optical solitons via bosonization, highlighting a novel duality in 1+1 dimensions.

## Key findings

- Thirring model fermions correspond to non-linear Schrödinger solitons in the non-relativistic limit.
- Optical solitons with Kerr non-linearity relate to fermionic particles in curved spacetime.
- The duality provides insights into fermion-soliton correspondence in low-dimensional quantum field theories.

## Abstract

Bosonization in curved spacetime maps massive Thirring model (self-interacting Dirac fermions) to a generalized sine-Gordon model, both living in $1+1$-dimensional curved spacetime. Applying this duality we have shown that the Thirring model fermion, in non-relativistic limit, gets identified with the soliton of non-linear Scrodinger model with Kerr form of non-linearity. We discuss one particular optical soliton in the latter model and relate it with the Thirring model fermion.