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Register a new userEquivalence of twistor prescriptions for super Yang-Mills
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There is evidence that one can compute tree level super Yang-Mills amplitudes using either connected or completely disconnected curves in twistor space. We argue that the two computations are equivalent, if the integration contours are chosen in a specific way, by showing that they can both be reduced to the same integral over a moduli space of singular curves. We also formulate a class of new ``intermediate prescriptions to calculate the same amplitudes.
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We consider the twistor space ${cal P}^6cong{mathbb R}^4{times}{mathbb C}P^1$ of ${mathbb R}^4$ with a non-integrable almost complex structure ${cal J}$ such that the canonical bundle of the almost complex manifold $({cal P}^6, {cal J})$ is trivial. It is shown that ${cal J}$-holomorphic Chern-Simons theory on a real $(6|2)$-dimensional graded extension ${cal P}^{6|2}$ of the twistor space ${cal P}^6$ is equivalent to self-dual Yang-Mills theory on Euclidean space ${mathbb R}^4$ with Lorentz invariant action. It is also shown that adding a local term to a Chern-Simons-type action on ${cal P}^{6|2}$, one can extend it to a twistor action describing full Yang-Mills theory.
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