Abstract. We first prove that, in Vasiliev's theory, the zero-form charges studied in 1103. 2360 and 1208.3880 are twisted open Wilson lines in the noncommutative Z space. This is shown by mapping Vasiliev's higher-spin model on noncommutative Yang-Mills theory. We then prove that, prior to Bose-symmetrising, the cyclically-symmetric higherspin invariants given by the leading order of these n-point zero-form charges are equal to corresponding cyclically-invariant building blocks of n-point correlation functions of bilinear operators in free conformal field theories (CFT) in three dimensions. On the higher spin gravity side, our computation reproduces the results of 1210.7963 using an alternative method amenable to the computation of subleading corrections obtained by perturbation theory in normal order. On the free CFT side, our proof involves the explicit computation of the separate cyclic building blocks of the correlation functions of n conserved currents in arbitrary dimension d > 2 using polarization vectors, which is an original result. It is shown to agree, for d = 3 , with the results obtained in 1301.3123 in various dimensions and where polarization spinors were used.
Efficient methods for describing non abelian charges in worldline approaches to QFT are useful to simplify calculations and address structural properties, as for example color/kinematics relations. Here we analyze in detail a method for treating arbitrary non abelian charges. We use Grassmann variables to take into account color degrees of freedom, which however are known to produce reducible representations of the color group. Then we couple them to a U(1) gauge field defined on the worldline, together with a Chern-Simons term, to achieve projection on an irreducible representation. Upon gauge fixing there remains a modulus, an angle parametrizing the U(1) Wilson loop, whose dependence is taken into account exactly in the propagator of the Grassmann variables. We test the method in simple examples, the scalar and spin 1/2 contribution to the gluon self energy, and suggest that it might simplify the analysis of more involved amplitudes.
Dedicated to the Memory of Víctor Manuel Villanueva Sandoval
We obtain a manifestly background independent BRST quantization of the N = 4 supersymmetric spinning particle. We show that nilpotency of the BRST charge Q implies the Einstein equations admitting a cosmological constant of indefinite sign. The physical graviton states are given by the vertex operator, obtained by an infinitesimal variation of Q, acting on diffeomorphism ghost states. In addition, the tree-point graviton scattering vertex is correctly reproduced by the worldline computation with these vertex operators.
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