Metric Reduction in Generalized Geometry and Balanced Topological Field Theories

TL;DR

This paper explores metric reduction in generalized geometry through supersymmetric sigma-models, connecting it to balanced topological field theories and analyzing Bismut connection reduction and generalized Kähler geometry on instanton moduli spaces.

Contribution

It provides a detailed geometric interpretation of metric reduction in generalized geometry using topological field theory formalism, including Bismut connection reduction and generalized Kähler geometry.

Findings

Detailed analysis of Bismut connection reduction.

Formal explanation of generalized Kähler geometry on instanton moduli spaces.

Connection between metric reduction and balanced topological field theories.

Abstract

The recently established metric reduction in generalized geometry is encoded in 0-dimensional supersymmetric $\sigma$-models. This is an example of balanced topological field theories. To find the geometric content of such models, the reduction of Bismut connections is studies in detail. Generalized K$\ddot{a}$hler reduction is briefly revisited in this formalism and the generalized K$\ddot{a}$hler geometry on the moduli space of instantons on a generalized K$\ddot{a}$hler 4-manifold of even type is thus explained formally in a topological field theoretic way.