Superconformal Field Theory In Six Dimensions And Supertwistor

Abstract

We studied the quantum dynamics of six dimensional $\mathcal{N}=(2,0)$ superconformal field theory (the QNG theory). We developed the spinor technique for six-dimensional quantum field theories. By combining this technique with the canonical quantization procedure, we can overcome the subtlety of the chiral nature of $\mathcal{N}=(2,0)$ free tensor multiplet and work out its quantum mechanical theory. We then studied the ${\mathbf{T}}^2$ compactification of the QNG theory and argued that the resulting four dimensional quantum field theory is indeed the $\mathcal{N}=4$ super-Yang-Mills theory with the $SL(2,\mathbf{Z})$ duality coming from the mapping class symmetries of ${\mathbf{T}}^2$. We also investigated the BPS self-dual string excitations by proposing a CFT description to their world sheet theory. At last, we constructed the super-twistor space $\widehat{\mathbb{PT}}$ that corresponded to the superconformal group $U^{\ast }Sp(4|2,\mathbf{H})\subset OSp(8|4,\mathbb{C})$, encoded the full free tensor multiplet into it and made some speculations on the possible super-twistor formulation of the QNG theory.

54 pages, 1 figures

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• An Alternative String Theory in Twistor Space for N=4 Super-Yang-Mills
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• TASI 2003 Lectures on AdS/CFT
• Higher-Dimensional Twistor Transforms using Pure Spinors
• The (2,0) supersymmetric theory of tensor multiplets and self-dual strings in six dimensions
• Scattering amplitudes for particles and strings in six-dimensional (2,0) theory
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Cited by in corpus (6)

• Dual Conformal Properties of Six-Dimensional Maximal Super Yang-Mills Amplitudes
• Conformal Field Theories in Six-Dimensional Twistor Space
• The polarized scattering equations for 6d superamplitudes
• On Twistors and Conformal Field Theories from Six Dimensions
• Ambitwistor Strings in Six and Five Dimensions
• The supersymmetric Penrose transform in six dimensions