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Journal Article

#### Metric- and frame-like higher-spin gauge theories in three dimensions

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##### Fulltext (public)

1408.2712.pdf

(Preprint), 295KB

JoPA_48_3_035402.pdf

(Preprint), 423KB

##### Supplementary Material (public)

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##### Citation

Fredenhagen, S., & Kessel, P. (2015). Metric- and frame-like higher-spin gauge
theories in three dimensions.* Journal of Physics A,* *48*(3):
035402. doi:10.1088/1751-8113/48/3/035402.

Cite as: http://hdl.handle.net/11858/00-001M-0000-0023-CCE3-F

##### Abstract

We study the relation between the frame-like and metric-like formulation of
higher-spin gauge theories in three space-time dimensions. We concentrate on
the theory that is described by an SL(3) x SL(3) Chern-Simons theory in the
frame-like formulation. The metric-like theory is obtained by eliminating the
generalised spin connection by its equation of motion, and by expressing
everything in terms of the metric and a spin-3 Fronsdal field. We give an exact
map between fields and gauge parameters in both formulations. To work out the
gauge transformations explicitly in terms of metric-like variables, we have to
make a perturbative expansion in the spin-3 field. We describe an algorithm how
to do this systematically, and we work out the gauge transformations to cubic
order in the spin-3 field. We use these results to determine the gauge algebra
to this order, and explain why the commutator of two spin-3 transformations
only closes on-shell.