Monday, October 17, 2005

CSW rules from YM light cone gauge

Gorsky and Rosly have a very interesting twistor paper today,

They consider Yang-Mills theory in the light-cone gauge and identify a non-local change of variables that implies, in a pretty straightforward fashion, the Cachazo-Svrček-Witten (CSW) "disconnected" rules for the Yang-Mills scattering amplitudes. Such an understanding of the problem allows them to conjecture that there should be a natural one-loop correction to the CSW Lagrangian, arising from the Jacobian of their field redefinition, and no higher-loop corrections.

Their method shows that the twistor techniques are not merely mysterious bricks included in the third road of quantum gravity - bricks that only magicians like Penrose can comprehend - but instead, they are components of the standard light-cone gauge and spinorial procedures used to work with the usual degrees of freedom.

They start with the Yang-Mills light-cone gauge which means

  • A+ = 0

and express the physical components of the Yang-Mills field

  • Ax +- i Ay
as "x+"-derivative or inverse derivative of two new scalar fields "phi+-", respectively. The Yang-Mills action then reduces to an action written entirely in terms of "phi+-". Moreover, we really want to set "phi-" equal to zero. It must be done together with a new field redefinition for "phi+" done in such a way that the (++-) vertex absent in the CSW action disappears.

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