Perturbative Gauge Theory as a String Theory in Twistor Space

By E. Witten. 2003

1,477 citations recorded by the source corpus.

Perturbative scattering amplitudes in Yang-Mills theory have many unexpected properties, such as holomorphy of the maximally helicity violating amplitudes. To interpret these results, we Fourier transform the scattering amplitudes from momentum space to twistor space, and argue that the transformed amplitudes are supported on certain holomorphic curves. This in turn is apparently a consequence of an equivalence between the perturbative expansion of = 4 super Yang-Mills theory and the D-instanton expansion of a certain string theory, namely the topological B model whose target space is the Calabi-Yau supermanifold

Subfields: Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

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Citations in the corpus

Supersymmetric gauge theories in twistor space (2006, methodology): “The kinetic terms and anti-selfdual interactions of N = 4 SYM theory may be described by a holomorphic Chern-Simons theory on PT(3|4) with action [1] S1[A] = i 2π ∫ Ω d(4)ψ ∧ tr { A∧ ∂A + 2 3 A∧A ∧A } (3.”
Topological M-theory as unification of form theories of gravity (2004, methodology): “One can complete T (M) to a Ricci-flat supermanifold by including extra fermionic directions [67].”
On the tree level S matrix of Yang-Mills theory (2004, background): “(As explained in [1], counting the fermionic modes reveals that the degree d is related to the total helicity ∑ hi of all n particles according to d = 1 2(n− ∑ hi−2).”
The all-loop integrand for scattering amplitudes in planar $ \mathcal{N} = 4 $ SYM (2010, methodology): “Witten’s 2003 proposal of twistor string theory [3] gave a strong impetus to rapid developments in the field, inspiring the development of powerful new tools for computing tree amplitudes, including CSW diagrams [4] and BCFW recursion relations [5–8].”
Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory (2009, methodology): “These would be the relevant operators for describing the coplanarity/collinearity properties found in [14].”
Gauge theory amplitudes in twistor space and holomorphic anomaly (2004, background): “ar X iv :h ep -t h/ 04 09 24 5v 1 2 4 Se p 20 04 Gauge Theory Amplitudes In Twistor Space And Holomorphic Anomaly Freddy Cachazo∗, Peter Svrček#, and Edward Witten∗ ∗ School of Natural Sciences, Institute for Advanced Study, Princeton NJ 08540 USA # Department of Physics, Joseph Henry…”
The complete planar S-matrix of $ \mathcal{N} = 4 $ SYM as a Wilson loop in twistor space (2010, background): “where S1 is a holomorphic Chern-Simons action [39, 40] S1[A] = ∫ CP3|4 D3|4Z ∧ Tr ( A ∂̄A+ 2 3 A(3) ) (3.”
One-loop gauge theory amplitudes in N=4 super Yang-Mills from MHV vertices (2004, methodology): “ques to calculate new tree amplitudes. One expects that this success will carry over to perturbative calculations at the loop level. Whilst some initial comments on loop diagrams were already made in [1] and, more recently, the twistor space structure of one-loop diagrams in N = 4 SYM has been analy”
Scattering amplitudes and Wilson loops in twistor space (2011, methodology): “Witten’s original twistor-string paper [42] also provides much excellent background and more.”
On the tensionless limit of string theory, off-shell higher spin interaction vertices and BCFW recursion relations (2010, methodology): “Such a method has appeared recently [42, 43] (BCFW) based upon the twistor formulation of gauge theories of Witten [39].”
Conformal basis for flat space amplitudes (2017, background): “One famous alternative basis is twistor space [1, 2] where many remarkable properties of perturbative gauge theory amplitudes are naturally explained.”
Loop amplitudes in gauge theories: modern analytic approaches (2010, background): “patible with, but lack, the − − + amplitude at tree level and the all-plus amplitude at one-loop. These amplitudes are not constructible from MHV diagrams but are also well localized in twistor space [74, 30]. Loop amplitudes in gauge theories: modern analytic approaches 25 Transformations have been”