A Twistor Space Action for Yang-Mills Theory

Abstract

We consider the twistor space ${\mathcal{P}}^6\cong {\mathbb{R}}^4\times \mathbb{C}{P}^1$ of ${\mathbb{R}}^4$ with a non-integrable almost complex structure $\mathcal{J}$ such that the canonical bundle of the almost complex manifold $({\mathcal{P}}^6,\mathcal{J})$ is trivial. It is shown that $\mathcal{J}$-holomorphic Chern-Simons theory on a real $(6|2)$-dimensional graded extension ${\mathcal{P}}^{6|2}$ of the twistor space ${\mathcal{P}}^6$ is equivalent to self-dual Yang-Mills theory on Euclidean space ${\mathbb{R}}^4$ with Lorentz invariant action. It is also shown that adding a local term to a Chern-Simons-type action on ${\mathcal{P}}^{6|2}$, one can extend it to a twistor action describing full Yang-Mills theory.

18 pages; v2: clarifying comments and a reference added, published version

References in corpus (4)

• Twistors, the ASD Yang-Mills equations, and 4d Chern-Simons theory
• Aspects of Twistor Geometry and Supersymmetric Field Theories within Superstring Theory
• Instantons on conical half-flat 6-manifolds
• On supertwistor geometry and integrability in super gauge theory

Cited by in corpus (3)

• Explicit Non-Abelian Gerbes with Connections
• Ambitwistor Yang-Mills Theory Revisited
• Quantizing local holomorphic field theories on twistor space