# General principles require that a massless vector couple to a conserved current?

I have a quote from Introduction to Bosonic Strings by Polchinski on page 28 which is presented below:

"General principles require that a massless vector couple to a conserved current and therefore that the theory have a gauge invariance. This is our first example of the massless gauge particles that are present in all fundamental string theories. Actually, this particular gauge boson, call it the photon, is not so interesting, because the gauge group is only $U(1)$ (there is only one photon) and because it turns out that all particles in the theory are neutral. [...] Similarly, a massless symmetric tensor particle must couple to a conserved symmetric tensor source. The only such source is the energy-momentum tensor; some additional possibilities arise in special cases, but these are not relevant here. Coupling to this in a consistent way requires the theory to have spacetime coordinate invariance. Thus the massless symmetric tensor is the graviton, and general relativity is contained as one small piece of the closed string theory. The massless antisymmetric tensor is known as a 2-form gauge boson."

I wish more detail from this one: "General principles require that a massless vector couple to a conserved current" and "a massless symmetric tensor particle must couple to a conserved symmetric tensor source". How does the general principles require all these? And what are the definitions of "massless vector" and "a massless symmetric tensor particle"?

A massless vector is the gauge field $A_\mu$ and the massless symmetric traceless tensor is the metric perturbation $h_{\mu\nu}$. They can couple only to conserved currents, namely the $U(1)$ vector current $j_\mu$ and the stress tensor $T_{\mu\nu}$ respectively. The requirement for this arises from gauge invariance.
Coupling a gauge field to a current means that in the Lagrangian, we include an interaction term of the form $${\cal L} \ni A_\mu j^\mu$$ Now, under gauge transformations $A_\mu \to A_\mu + \partial_\mu \alpha$ for some arbitrary function $\alpha(x)$. The action then transforms as $${\cal L} \to {\cal L} + \partial_\mu \alpha j^\mu$$ For the action to be invariant under gauge transformations, it had better be that the term above be a total derivative. This can only happen if $j^\mu$ is a conserved current.