Duality and Bosonisation in Arbitrary Dimensions

TL;DR

This paper develops a functional integral approach to bosonisation in arbitrary dimensions, revealing dualities between fermionic and bosonic models, including gauge and tensor fields, and reproduces known results in lower dimensions.

Contribution

It introduces a general bosonisation framework for arbitrary dimensions, establishing dualities between fermionic models and gauge or tensor field theories, extending previous lower-dimensional results.

Findings

Bosonisation maps fermionic models to gauge and tensor field theories in all dimensions.

Establishes duality between the Proca model and the Kalb-Ramond tensor model.

Reproduces known bosonisation results in D=2 and D=3.

Abstract

A functional integral approach is developed to discuss the bosonisation of the massive Thirring and the massive Schwinger models in arbitrary D-dimensions. It is found that these models, to {\it all} orders in the inverse fermi mass, bosonise to a theory involving a usual gauge field and a (D-2) rank antisymmetric (Kalb-Ramond) tensor field. Explicit bosonisation identities for the fermion current are deduced. Specialising to the lowest order reveals (for any $D \geq 4$) a mapping between the massive Thirring model and the Proca model. It also establishes an exact duality between the Proca model and the massive (D-2) rank Kalb-Ramond model. Schwinger terms in the current algebra are computed. Conventional bosonisation results in D=2, 3 are reproduced.