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

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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?

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

This post imported from StackExchange Physics at 2016-03-13 14:30 (UTC), posted by SE-user phy_math
Do you have a link to the talk/a paper by the speaker?

This post imported from StackExchange Physics at 2016-03-13 14:30 (UTC), posted by SE-user innisfree
I have no idea what the two theorems you are referring to are supposed to be. The Weinberg-Witten theorem makes a statement about massless conserved currents and stress energies, not about "higher spin amplitudes". The Coleman-Mandula theorem states that there are no non-gauge symmetries except for the Poincaré symmetry, but since spin is essentially the conserved charge of the Lorentz symmetry, I do not see why you say "there is no conserved higher spin".

This post imported from StackExchange Physics at 2016-03-13 14:30 (UTC), posted by SE-user ACuriousMind
@ACuriousMind, innisfree, i am refering, talk by Xi Yin.

This post imported from StackExchange Physics at 2016-03-13 14:30 (UTC), posted by SE-user phy_math
I'm not an expert on higher spin theories but I've heard similar statements being made. A simple observation that may or may not be relevant is that the theorems you are talking about (Weinberg soft limit for massless spin-s particles, Weinberg-Witten, Coleman Mandela) all assume a Poincaire invariant vacuum state. AdS is not Poincaire invariant, meaning the symmetry group of AdS is not the Poincaire group ISO(1,3). So the speaker may be saying that the theorems don't apply on AdS because the vacuum isn't Poincaire invariant. Again, I'm not an expert so there may be more to it than that.

This post imported from StackExchange Physics at 2016-03-13 14:30 (UTC), posted by SE-user Andrew
+1 though, if there is a real expert on higher spin on these forums I'd love to hear a fuller explanation.

This post imported from StackExchange Physics at 2016-03-13 14:30 (UTC), posted by SE-user Andrew
I looked into this and found that a) Weinberg's theorem is derived from a factorization property of the S-matrix, not Lorentz invariance itself and b) it's not "higher spin" that can't be conserved, it's a current/charge with higher spin (you did not copy that correctly from the talk). I edited those corrections in.

This post imported from StackExchange Physics at 2016-03-13 14:30 (UTC), posted by SE-user ACuriousMind

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