Abstract
We present the inverse Penrose transform (the map from spacetime to twistor space) for self-dual Yang-Mills (SDYM) and its higher-spin extensions on a flat background. The twistor action for the higher-spin extension of SDYM (HS-SDYM) is of mathcal{BF} -type. By considering a deformation away from the self-dual sector of HS-SDYM, we discover a new action that describes a higher-spin extension of Yang-Mills theory (HS-YM). The twistor action for HS-YM is a straightforward generalization of the Yang-Mills one.
Highlights
PT is the projective twistor space, and M4 is the four-dimensional flat spacetime
We present the inverse Penrose transform for self-dual Yang-Mills (SDYM) and its higher-spin extensions on a flat background
One may expect to discover another class of higher spin gravity (HSGRA) by deforming the chiral theories to what we do to SDYM and SDGRA
Summary
Let us recall that a massless field of helicity h in M4 can be represented by a cohomology class, say ω, of Dolbeault cohomology group H0,1(PT, O(2h − 2)) on twistor space We will need to use one more result in twistor theory It is proven in [40, 43, 44] that a gauge potential Φα(n),α that describes a free field of positive helicity and obeys ∂αα Φα(n),α = 0 is represented by A ∈ H0,1(PT, O(n − 1)). Another way to phrase this result is. For more on the light-cone gauge approach, see [12,13,14,15]
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