3-dimensional scalar-vector dual of topological sigma-model

TL;DR

This paper introduces a 3D dual model to the Rozansky-Witten topological sigma-model, showing that its classical partition function computes the Milnor linking number, linking topological invariants with quantum field theory.

Contribution

It presents a novel 3D scalar-vector dual model for the Rozansky-Witten sigma-model and connects its classical partition function to Milnor linking numbers.

Findings

Feynman diagram calculations reproduce Milnor linking number

Establishment of a duality between models in different dimensions

Linking topological invariants with classical partition functions

Abstract

A 3-dimensional model dual to the Rozansky-Witten topological sigma-model with a hyper-Kaehler target space is considered. It is demonstrated that a Feynman diagram calculation of the classical part of its partition function yields the Milnor linking number.