nLab twistor string theory



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It seems (Nair 1988, Witten 2004, Sec. 3) that the scattering amplitudes of nn gluons (n-point functions) in pure Yang-Mills theory on 4d Minkowski spacetime, regarded as distributions on the product space of nn copies of twistor space P 3 \mathbb{C}P^3 , have support – after complexification – on (the diagonal image of) a complex curve in twistor space, hence on the image of a holomorphic function

(1)ϕ:ΣP 3 \phi \;\colon\; \Sigma \longrightarrow \mathbb{C}P^3

from a Riemann surface Σ\Sigma to complex projective 3-space. Here the genus gg of Σ\Sigma is bounded by the loop order ll of the scattering amplitude, glg \leq l and the degree of the map (1) depends on the number qq of negative helicity gluon states in the process, as d=q1+ld \,=\, q - 1 + l.

The idea of twistor string theory is to understand these complex curves in twistor space as worldsheet instantons (or rather D1-brane-instantons) of a string theory – specifically of the B-model topological string, whose target space is the twistor space P 3 \mathbb{C}P^3 , or rather the supermanifold 3|4\mathbb{C}^{3\vert 4} – and to use this to explain the structure of MHV amplitudes in N=4 D=4 super Yang-Mills theory.

Somehow. The original proposals (Witten 04, Berkovits 04) were only partially succesful as string theories (e.g. Skinner 09, Spradlin).

But the idea as such of scattering amplitudes localized on complex curves in twistor space remains fruitful in pure quantum field theory, for instance it seems to generalize to perturbative quantum gravity in the form of D=4 N=8 supergravity (Cachazo & Skinner 2012).



Original articles:


Further developments:

  • Yvonne Geyer, Arthur E. Lipstein, Lionel Mason, Ambitwistor strings in 4-dimensions, Phys. Rev. Lett. 113, 081602 (2014) (arXiv:1404.6219)

Discussion for D=4 N=8 supergravity:

Last revised on August 13, 2021 at 11:40:47. See the history of this page for a list of all contributions to it.