On Twistors and Conformal Field Theories from Six Dimensions

Abstract

We discuss chiral zero-rest-mass field equations on six-dimensional space-time from a twistorial point of view. Specifically, we present a detailed cohomological analysis, develop both Penrose and Penrose-Ward transforms, and analyse the corresponding contour integral formulae. We also give twistor space action principles. We then dimensionally reduce the twistor space of six-dimensional space-time to obtain twistor formulations of various theories in lower dimensions. Besides well-known twistor spaces, we also find a novel twistor space amongst these reductions, which turns out to be suitable for a twistorial description of self-dual strings. For these reduced twistor spaces, we explain the Penrose and Penrose-Ward transforms as well as contour integral formulae.

v4: 66 pages, typos fixed, appendix B revised

References in corpus (15)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Gauge Symmetry and Supersymmetry of Multiple M2-Branes
• Algebraic structures on parallel M2-branes
• Amplitudes and Spinor-Helicity in Six Dimensions
• (1,0) superconformal models in six dimensions
• Non-Abelian Tensor Multiplet Equations from Twistor Space
• Amplitudes of 3D and 6D Maximal Superconformal Theories in Supertwistor Space
• Conformal Field Theories in Six-Dimensional Twistor Space
• Amplitudes for Multiple M5 Branes
• N=6 Superspace Constraints, SUSY Enhancement and Monopole Operators
• N=8 Superspace Constraints for Three-dimensional Gauge Theories
• The 3-Lie Algebra (2,0) Tensor Multiplet and Equations of Motion on Loop Space
• Constructing Self-Dual Strings
• Hidden Symmetries and Integrable Hierarchy of the N=4 Supersymmetric Yang-Mills Equations
• A Twistor Description of Six-Dimensional N=(1,1) Super Yang-Mills Theory

Cited by in corpus (23)

• $L_{\infty }$-Algebras of Classical Field Theories and the Batalin-Vilkovisky Formalism
• Non-Abelian Tensor Towers and (2,0) Superconformal 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
• Twistor methods for AdS${}_5$
• Semistrict Higher Gauge Theory
• Higher Groupoid Bundles, Higher Spaces, and Self-Dual Tensor Field Equations
• $L_{\infty }$-Algebras, the BV Formalism, and Classical Fields
• Geometrical Aspects of An Abelian (2,0) Action
• Non-abelian Self-Dual String and M2-M5 Branes Intersection in Supergravity
• Lessons from M2's and Hopes for M5's
• The Non-Abelian Self-Dual String and the (2,0)-Theory
• Spinor description of $D=5$ massless low-spin gauge fields
• Supersymmetric Yang-Mills Theory as Higher Chern-Simons Theory
• Spinors and the Weyl Tensor Classification in Six Dimensions
• Instantons on the six-sphere and twistors
• Instantons in six dimensions and twistors
• On the Six-dimensional Kerr Theorem and Twistor Equation
• Massless chiral fields in six dimensions
• Conformally Invariant Spinorial Equations in Six Dimensions
• Explicit Non-Abelian Gerbes with Connections
• Twisted Weil Algebras for the String Lie 2-Algebra