Six-Dimensional Superconformal Field Theories from Principal 3-Bundles over Twistor Space

Abstract

We construct manifestly superconformal field theories in six dimensions which contain a non-Abelian tensor multiplet. In particular, we show how principal 3-bundles over a suitable twistor space encode solutions to these self-dual tensor field theories via a Penrose-Ward transform. The resulting higher or categorified gauge theories significantly generalise those obtained previously from principal 2-bundles in that the so-called Peiffer identity is relaxed in a systematic fashion. This transform also exposes various unexplored structures of higher gauge theories modelled on principal 3-bundles such as the relevant gauge transformations. This enables us to formulate the non-Abelian differential cohomology that describes principal 3-bundles with connective structures.

v3: 45 pages, improved presentation, published version

References in corpus (10)

• A Non-Abelian Self-Dual Gauge Theory in 5+1 Dimensions
• Six-dimensional superconformal couplings of non-abelian tensor and hypermultiplets
• A Kaluza-Klein inspired action for chiral p-forms and their anomalies
• M-brane Models from Non-Abelian Gerbes
• Self-Dual Supergravity and Twistor Theory
• N=8 Superspace Constraints for Three-dimensional Gauge Theories
• Duality-symmetric actions for non-Abelian tensor fields
• Non-abelian Self-Dual String and M2-M5 Branes Intersection in Supergravity
• Non-Abelian Self-Dual String Solutions
• Instantons in six dimensions and twistors

Cited by in corpus (35)

• The $(2,0)$ superconformal bootstrap
• $L_{\infty }$-Algebras of Classical Field Theories and the Batalin-Vilkovisky Formalism
• Global 3-group symmetry and 't Hooft anomalies in axion electrodynamics
• Global 4-group symmetry and 't Hooft anomalies in topological axion electrodynamics
• $D=6$, $\mathcal{N}=(2,0)$ and $\mathcal{N}=(4,0)$ theories
• Towards an M5-Brane Model I: A 6d Superconformal Field Theory
• Six-Dimensional (1,0) Superconformal Models and Higher Gauge Theory
• Construction of 6D supersymmetric field models in N=(1,0) harmonic superspace
• Semistrict Higher Gauge Theory
• Higher Groupoid Bundles, Higher Spaces, and Self-Dual Tensor Field Equations
• $L_{\infty }$-Algebras, the BV Formalism, and Classical Fields
• On $3$-gauge transformations, $3$-curvature and $\mathbf{Gray}$-categories
• Lattice Gerbe Theory
• Towards an M5-Brane Model II: Metric String Structures
• $L_{\infty }$-Algebra Models and Higher Chern-Simons Theories
• A Lie based 4-dimensional higher Chern-Simons theory
• The Non-Abelian Self-Dual String and the (2,0)-Theory
• Canonical gauges in higher gauge theory
• Generalized Higher Gauge Theory
• Aspects of Effective Theory for Multiple M5-Branes Compactified On Circle
• Higher Poincare Lemma and Integrability
• Topological invariant of 4-manifolds based on a 3-group
• Supersymmetric Yang-Mills Theory as Higher Chern-Simons Theory
• BCF anomaly and higher-group structure in the low energy effective theories of mesons
• Higher form Yang-Mills as higher BFYM theories
• Higher Gauge Theory
• 3-form Yang-Mills based on 2-crossed modules
• Gauge symmetry of the 3BF theory for a generic Lie 3-group
• On the global $2$-holonomy for a $2$-connection on a $2$-bundle
• Higher Chern-Simons based on (2-)crossed modules
• Henneaux-Teitelboim gauge symmetry and its applications to higher gauge theories
• Symmetry breaking mechanisms of the 3BF action for the Standard Model coupled to gravity
• Dual infrared limits of 6d $\mathcal{N}$=(2,0) theory
• Correspondence between 3BF and Einstein-Cartan formulations of quantum gravity
• Explicit Non-Abelian Gerbes with Connections