How does higher spin theory evade Weinberg's and the Coleman-Mandula no-go theorem?

Question

Recently I heard some seminar on higher spin gauge theory, and got some interest. I know there are some no-go theorems in quantum field theories:

Weinberg: Massless higher spin amplitudes are forbidden by the general form of the S-mastrix.

Coleman-Mandula: There is no conserved higher spin charge/current, considering nontrivial S-matrix and mass gap formalism.

The speaker says, that by introducing a cosmological constant, i.e. introducing AdS space, one can avoid these no go theorems, but I am not sure how.

Can you give me some explanation for this?

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My reference is a talk by Xi Yin, page 5.

Answer 1

The Weinberg's statement is often rephrased as:

"There are no interacting theories of massless particles of spin greater than 2"

You can show this assuming only little group invariance and soft limits, without needing a lagrangian description. In a naive fashion, higher spin theories evade this theorem by including an infinite number of massless higher spin fields. This is reminiscent of string theory, in which an infinite number of fields give you a soft behaviour for scattering amplitudes, while a single field of higher spin tend to give divergent contribution going like $\frac{s^J}{s-M^2}$ where $s$ is the usual Mandelstam variable.

This reference could be helpful: http://arxiv.org/abs/1007.0435