Instantons, Twistors, and Emergent Gravity
Motivated by potential applications to holography on space-times of positive curvature, and by the successful twistor description of scattering amplitudes, we propose a new dual matrix formulation of N = 4 gauge theory on S 4 . The matrix model is defined by taking the low energy limit of a holomorphic Chern-Simons theory on CP 3|4 , in the presence of a large instanton flux. The theory comes with a choice of S 4 radius l and a parameter N controlling the overall size of the matrices. The flat space variant of the 4D effective theory arises by taking the large N scaling limit of the matrix model, with l 2 ∼ l 2 /N held fixed. Its massless spectrum contains both spin one and spin two excitations, which we identify with gluons and gravitons. As shown in the companion paper [1], the matrix model correlation functions of both these excitations correctly reproduce the corresponding MHV scattering amplitudes. We present evidence that the scaling limit defines a gravitational theory with a finite Planck length. In particular we find that in the lpl → 0 limit, the matrix model makes contact with the CSW rules for amplitudes of pure gauge theory, which are uncontaminated by conformal supergravity. We also propose a UV completion for the system by embedding the matrix model in the physical superstring.