Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2003-12-15
Commun.Math.Phys.252:189-258,2004
Physics
High Energy Physics
High Energy Physics - Theory
97 pp
Scientific paper
10.1007/s00220-004-1187-3
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 ${\cal N}=4$ 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 $\Bbb{CP}^{3|4}$.
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