Coordinate-free action for AdS3 higher-spin-matter systems

A coordinate-free action principle for the N=2 supersymmetric model of spin 0 and spin 1/2 matter fields interacting via Chern–Simons higher spin gauge fields in AdS3 is formulated in terms of star-product algebra of two oscillators. Although describing proper relativistic dynamics the action does not contain space-time coordinates. It is given by a supertrace of a forth-order polynomial in the 3d higher spin superalgebra. The theory admits a free parameter characterizing the inequivalent vacua associated with the parameter of mass m of the matter fields. For the case of the massless matter, the model has a form of the noncommutative 2d Yang–Mills theory with some infinite-dimensional gauge group. The limit m→∞ corresponds to the SU(∞) 2d Yang–Mills theory.