What does Weinberg–Witten theorem want to express?

[Ganesh Ujwal]

Weinberg-Witten theorem states that massless particles (either composite or elementary) with spin $j > 1/2$ cannot carry a Lorentz-covariant current, while massless particles with spin $j > 1$ cannot carry a Lorentz-covariant stress-energy. The theorem is usually interpreted to mean that the graviton ($j = 2$) cannot be a composite particle in a relativistic quantum field theory.

While the argument is so strong and weird, how is it possible? Why can we not construct a theory which is massless charged vector field and therefore carry a Lorentz-covariant current ? And although we assume the second argument is right, which says massless particles with spin $j > 1$ cannot carry a Lorentz-covariant stress-energy, how does it imply that the graviton ($j = 2$) cannot be a composite particle ?

 

[atyy]

The Weinberg-Witten theorem implies that the graviton is not composite, because quantum fields usually have Lorentz-covariant stress-energy, and composite particles made from such fields will also have Lorentz-covariant stress-energy.

There is an interesting note in the Weinberg-Witten paper that the theorem does not exclude emergent gravity approaches like Sakharov's, because there the emergence is from quantum corrections, and not from composite particles.