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Counting of degrees of freedom in Higher Spin Theories in curved spacetime

There are several definitions of the number of physical degrees of freedom with varying degree of applicability. Once you have a theory in one of the maximally symmetric spaces (Minkowski, de Sitter, ...
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Number of independent reparametrization gauge invariances of the 'world $(n+1)$-manifold action' of $n$-dimensional objects

GSW is merely stating the fact that an $(n+1)$-dimensional world volume has $(n+1)$-dimensional local coordinate systems, or equivalently, is parametrized by $n+1$ independent parameters $\sigma^{\...
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