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There are soft theorems that suggest that any massless boson with spin higher than 2 should be a free field theory and cannot have interactions. Does this mean that one cannot embed such fields into a theory with gravity, which naturally interacts with anything with a stress-energy?

Qmechanic
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Panopticon
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1 Answers1

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When you have a higher spin field, it will, in principle, have a stress-energy tensor, and since gravity couples to the stress-energy tensor, it should follow that gravity will naturally couple to this field.

The Question

You clarified your question in a comment, I will highlight below:

"My question is whether the soft theorems rule out [the] situation [of the form of the couplings is totally fixed by the graviton's universal coupling to the stress-energy tensor], even when you put no explicit coupling between the higher spin bosons in the theory."

Simply put, can we predict or explain if gravity fails to interact with other fields even when no explicit coupling is introduced? And, do the soft theorems rule out interactions even if there's no explicit coupling introduced?

My answer

While soft theorems don't rule out interactions entirely, they place strict constraints on their form and strength. So, while you might not introduce a direct coupling, it must be remembered that the dynamics of the theory, especially in the context of gravity, can lead to emergent interactions that must still obey these constraints.

Gabriel Fair
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