We construct and study the 6D dual superconformal algebra. Our construction is inspired by the dual superconformal symmetry of massless 4D ##IMG## [http://ej.iop.org/images/1751-8121/53/27/275402/aab8ff6ieqn2.gif] {$\mathcal{N}=4$} SYM and extends the previous construction of the enhanced dual conformal algebra for 6D ##IMG## [http://ej.iop.org/images/1751-8121/53/27/275402/aab8ff6ieqn3.gif] {$\mathcal{N}=\left(1,1\right)$} SYM to the full 6D dual superconformal algebra for chiral theories. We formulate constraints in 6D spinor helicity formalism and find all generators of the 6D dual superconformal algebra. Next, we check that they agree with the dual superconformal generators of known 3D and 4D theories. We show that it is possible to significantly simplify the form of generators and compactly write the dual superconformal algebra using superindices. Finally, we work out some examples of algebra invariants.

中文翻译：

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6D对偶超保形代数

我们构建和研究6D对偶超保形代数。我们的构造受到无质量4D的双重超共形对称性的启发## IMG ## [http://ej.iop.org/images/1751-8121/53/27/275402/aab8ff6ieqn2.gif] {$ \ mathcal {N } = 4 $} SYM，并扩展了用于6D的增强型双保形代数的先前构造## IMG ## [http://ej.iop.org/images/1751-8121/53/27/275402/aab8ff6ieqn3.gif ] {$ \ mathcal {N} = \ left（1,1 \ right）$} SYM到用于手性理论的完整6D对偶超保形代数。我们在6D旋子螺旋度形式主义中制定约束条件，并找到6D对偶超保形代数的所有生成器。接下来，我们检查它们是否与已知3D和4D理论的双重超保形发生器一致。我们表明，可以显着简化生成器的形式，并使用超指数紧凑地编写对偶超保形代数。最后，我们得出一些代数不变量的例子。