The non-linear coupled spin 2 - spin 3 Cotton equation in three dimensions
Journal article, 2016

In the context of three-dimensional conformal higher spin theory we derive, in the frame field formulation, the full non-linear spin 3 Cotton equation coupled to spin 2. This is done by solving the corresponding Chern-Simons gauge theory system of equations, that is, using F=0 to eliminate all auxiliary fields and thus expressing the Cotton equation in terms of just the spin 3 frame field and spin 2 covariant derivatives and tensors (Schouten). In this derivation we neglect the spin 4 and higher spin sectors and approximate the star product commutator by a Poisson bracket. The resulting spin 3 Cotton equation is complicated but can be related to linearized versions in the metric formulation obtained previously by other authors. The expected symmetry (spin 3 "translation", "Lorentz" and "dilatation") properties are verified for Cotton and other relevant tensors but some perhaps unexpected features emerge in the process, in particular in relation to the non-linear equations. We discuss the structure of this non-linear spin 3 Cotton equation but its explicit form is only presented here, in an exact but not completely refined version, in appended files obtained by computer algebra methods. Both the frame field and metric formulations are provided.

Higher Spin Symmetry

Conformal Field Models in String Theory

Chern-Simons Theories

AdS-CFT Correspondence

Author

Hampus Linander

Chalmers, Physics, Theoretical Physics

Bengt E W Nilsson

Chalmers, Physics, Theoretical Physics

Journal of High Energy Physics

1126-6708 (ISSN) 1029-8479 (eISSN)

Vol. 2016 7 24

Roots

Basic sciences

Subject Categories

Other Physics Topics

DOI

10.1007/JHEP07(2016)024

More information

Latest update

12/2/2022