Abstract
We show that the off-shell N=3 action of N=4 super Yang-Mills can be written as a holomorphic Chern-Simons action whose Dolbeault operator is constructed from a complex-real (CR) structure of harmonic space. We also show that the local space-time operators can be written as a Penrose transform on the coset SU(3)/(U(1) \times U(1)). We observe a strong similarity to ambitwistor space constructions.
Highlights
We show that the off-shell N = 3 action of N = 4 super Yang-Mills can be written as a holomorphic Chern-Simons action whose Dolbeault operator ∂ ̄ is constructed from a complex-real (CR) structure of harmonic space
We show that the local spacetime operators can be written as a Penrose transform on the coset SU(3)/(U(1) × U(1))
Korchemsky, Maldacena and Sokatchev have shown that in this light-like limit one can extract the same information contained in the scattering amplitudes and in the Wilson loops. An understanding of this new equivalence from the twistor point of view was provided in ref. [23] by considering correlation functions of Konishi operators
Summary
Before we go on to discuss concrete examples, let us describe the basic strategy in the harmonic superspace constructions. Finding a manifold M with a CR structure which is preserved by G is not necessarily straightforward, but it can be suggested by the usual analysis of constraints Using this data we build a field theory of a connection A on M which is holomorphic Chern-Simons, and which has the right symmetries.. The constraints involving the fermionic covariant derivatives can be solved by going to a gauge where their connections vanish (which is possible because they are flat). These constraints can be written explicitly and an action from which they follow as equations of motion can be found This is where our approach differs from the usual treatment, in order to get the holomorphic Chern-Simons action, we will think of these connections as components of a differential one-form, defined as. It is worth noting that if we write the action in terms of component fields A(1,−2), A(2,−1) and A(1,1) the symmetry algebra is much harder to guess
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