Topological Matter in Two Dimensions

TL;DR

This paper constructs two-dimensional topological quantum field theories with matter by twisting N=2 supersymmetric theories, revealing connections to sigma models, Landau-Ginzburg theories, and topological gravity.

Contribution

It demonstrates how different N=2 multiplets produce distinct classes of topological theories and formulates 2D topological gravity via a gauge principle applied to the twisted algebra.

Findings

N=2 chiral multiplets lead to topological sigma models

N=2 twisted chiral multiplets produce Landau-Ginzburg theories

Topological gravity is formulated using a gauge principle

Abstract

Topological quantum field theories containing matter fields are constructed by twisting $N=2$ supersymmetric quantum field theories. It is shown that $N=2$ chiral (antichiral) multiplets lead to topological sigma models while $N=2$ twisted chiral (twisted antichiral) multiplets lead to Landau-Ginzburg type topological quantum field theories. In addition, topological gravity in two dimensions is formulated using a gauge principle applied to the topological algebra which results after the twisting of $N=2$ supersymmetry.