Supersymmetric Yang-Mills Theory as Higher Chern-Simons Theory

Abstract

We observe that the string field theory actions for the topological sigma models describe higher or categorified Chern-Simons theories. These theories yield dynamical equations for connective structures on higher principal bundles. As a special case, we consider holomorphic higher Chern-Simons theory on the ambitwistor space of four-dimensional space-time. In particular, we propose a higher ambitwistor space action functional for maximally supersymmetric Yang-Mills theory.

v2: 25 pages, conventions improved, typos fixed, published version

References in corpus (5)

• Semistrict Higher Gauge Theory
• Higher Groupoid Bundles, Higher Spaces, and Self-Dual Tensor Field Equations
• 4-d semistrict higher Chern-Simons theory I
• Topological String Theory Revisited I: The Stage
• Topological Sigma Models On Supermanifolds

Cited by in corpus (8)

• $L_{\infty }$-Algebras of Classical Field Theories and the Batalin-Vilkovisky Formalism
• $L_{\infty }$-Algebras, the BV Formalism, and Classical Fields
• Topological invariant of 4-manifolds based on a 3-group
• Higher Gauge Theory
• Symmetry breaking mechanisms of the 3BF action for the Standard Model coupled to gravity
• Explicit Non-Abelian Gerbes with Connections
• Correspondence between 3BF and Einstein-Cartan formulations of quantum gravity
• Ambitwistor Yang-Mills Theory Revisited