Coordinate-Free Action for AdS3 Higher-Spin-Matter Systems

TL;DR

This paper develops a coordinate-free, star-product algebra-based action principle for an N=2 supersymmetric higher-spin matter system in AdS3, revealing connections to noncommutative 2D Yang-Mills theories.

Contribution

It introduces a novel coordinate-free formulation of higher-spin matter interactions in AdS3 using star-product algebra, linking to noncommutative gauge theories.

Findings

The action is expressed as a supertrace of a polynomial in the higher spin superalgebra.

The model includes a free parameter related to matter mass, affecting vacuum structure.

Massless case reduces to a noncommutative 2D Yang-Mills theory.

Abstract

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\to\infty corresponds to the SU(\infty) 2d Yang-Mills theory.