Topological twisting of conformal supercharges

TL;DR

This paper explores the topological twisting of N=4 super Yang-Mills theory on curved four-manifolds, identifying conditions under which conformal supercharges are preserved and constructing a related topological field theory.

Contribution

It demonstrates that on conical four-manifolds, exactly two conformal supercharges remain unbroken and formulates a topological theory with a family of supercharges parameterized by CP^1.

Findings

Two conformal supercharges remain on conical manifolds

Constructed off-shell formulation with a CP^1 family of topological charges

The theory is metric-independent on the base three-manifold

Abstract

Putting a twisted version of N=4 super Yang-Mills on a curved four-dimensional manifold generically breaks all conformal supersymmetries. In the special case where the four-manifold is a cone, we show that exactly two conformal supercharges remain unbroken. We construct an off-shell formulation of the theory such that the two unbroken conformal supercharges combine into a family of topological charges parameterized by CP^1. The resulting theory is topological in the sense that it is independent of the metric on the three-dimensional base of the cone.