Weinberg-Witten theorem states that massless particles (either composite or elementary) with spin [latex]j > 1/2[/latex] cannot carry a Lorentz-covariant current, while massless particles with spin [latex]j > 1[/latex] cannot carry a Lorentz-covariant stress-energy. The theorem is usually interpreted to mean that the graviton ([latex]j = 2[/latex]) 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 [latex]j > 1[/latex] cannot carry a Lorentz-covariant stress-energy, how does it imply that the graviton ([latex]j = 2[/latex]) cannot be a composite particle ?

I have not looked at this properly, but loosely the theorem says that higher spin particle cannot couple to gravity in a consistent way. You can find some notes on the Weinberg-Witten theorem in David Bailin's website. He gave a talk about this a while ago that I attended.

 

http://www.phys.susx.ac.uk/~mpfg9/