TY - JOUR

T1 - Twistor-like transform in ten dimensions

AU - Witten, Edward

N1 - Funding Information:
It is almost certainly not reasonable to expect an equally powerful transformation of the second order Einstein or Yang-Mills equations. One cannot expect these equations, which describe non-trivial scattering processes, to be integrable**. Nevertheless, there is a twistor-like transform \[6, 7\] of the second order Yang-Mills equations. It is much less powerful than the twistor transform of the self-dual equations because it involves light-like lines rather than null planes. It does not * Research supported in part by NSF Grant PHY80-19754. ** Under appropriate conditions, a solution of a nonlinear classical equation has free field behavior in the far past or far future. The transformation from the free field data in the far past to the Pree field data in the far future might be called the classical S transformation, ,.~. Although the details have never been developed, one may expect that a classical analogue of the Coleman-Mandula theorem \[5\]i mplies S = 1 for integrable classical theories in more than 1 + 1 dimensions. The twistor transform can indeed be used to show that S = I for the self-dual theories that are integrable. But the second order Einstein and Yang-Mills equations certainly have ..q # 1, since there is nontrivial newtonian or coulombic scattering of wave packets that collide with very large impact parameters.

PY - 1986/3/17

Y1 - 1986/3/17

N2 - A twistor-like transform of ten-dimensional supersymmetric Yang-Mills theory is described. It generalizes previous work on N = 4 supersymmetric Yang-Mills theory in four dimensions. Partial results are obtained concerning a twistorial transform of N = 1 supergravity in ten dimensions. The motivation for this work is the possibility that the twistor transform of ten-dimensional supersymmetric field theory is the proper starting point for understanding the geometrical meaning of superstring theory. Developing the twistor transform requires developing the needed tools for coupling a superstring to a background supergravity field; this coupling is described in the last section.

AB - A twistor-like transform of ten-dimensional supersymmetric Yang-Mills theory is described. It generalizes previous work on N = 4 supersymmetric Yang-Mills theory in four dimensions. Partial results are obtained concerning a twistorial transform of N = 1 supergravity in ten dimensions. The motivation for this work is the possibility that the twistor transform of ten-dimensional supersymmetric field theory is the proper starting point for understanding the geometrical meaning of superstring theory. Developing the twistor transform requires developing the needed tools for coupling a superstring to a background supergravity field; this coupling is described in the last section.

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U2 - 10.1016/0550-3213(86)90090-8

DO - 10.1016/0550-3213(86)90090-8

M3 - Article

AN - SCOPUS:33750534822

SN - 0550-3213

VL - 266

SP - 245

EP - 264

JO - Nuclear Physics, Section B

JF - Nuclear Physics, Section B

IS - 2

ER -