Abstract
This paper presents a worldsheet theory describing holomorphic maps to twistor space with mathcal{N} fermionic directions. The theory is anomaly free when mathcal{N} = 8. Via the Penrose transform, the vertex operators correspond to an mathcal{N} = 8 Einstein supergravity multiplet. In the first instance, the theory describes gauged supergravity in AdS4. Upon taking the flat space, ungauged limit, the complete classical S-matrix is recovered from worldsheet correlation functions.
Highlights
The most influential scattering amplitude in Yang-Mills theory is undoubtedly the Parke-Taylor amplitude [1] An,0 =i, j 4 δ4( i pi) 1, 2 2, 3 · · · n, 1 (1.1)It describes the tree-level scattering of two gluons i and j of negative helicity and n − 2 gluons of positive helicity, each of momentum pi = λiλi
This paper presents a worldsheet theory describing holomorphic maps to twistor space with N fermionic directions
Combining the correlation functions (4.25) & (4.37) with the remaining integral over the zero modes of the Y Z system — i.e., the space of holomorphic maps Z : Σ → PT — and dividing by vol(GL(2; C)) to account for the zero modes of the ghosts associated to the worldsheet gauge theory, we have found that d+2 n d δ2(γ) hi(Z)
Summary
The most influential scattering amplitude in Yang-Mills theory is undoubtedly the Parke-. One outcome of these investigations was given in [32], where it was conjectured that arbitrary n-particle NkMHV tree-level amplitudes in N = 8 supergravity could be represented as This form was obtained by interpreting (1.3) in terms degree 1 holomorphic maps from a Riemann sphere Σ into twistor space, and generalizing to higher degree maps. It is worth pointing out immediately that the present model is more successful than the original twistor strings [12, 56] were (as a theory of pure N = 4 SYM) in at least one respect: the worldsheet correlator we consider leads inexorably to (1.5) and only to (1.5). It seems likely that the relation will be somewhat similar to that between the RNS and pure spinor versions of full string theory [75]
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