Massless closed-string vertex operator
= Massless closed-string vertex operator
At the first massless closed-string level, the matter vertex has the form $\epsilon_{\mu\nu}:\!\partial X^\mu\bar\partial X^\nu e^{ik\cdot X}\!:$, with null momentum and a polarization tensor transverse in both indices. Its symmetric trace-free, antisymmetric and trace sectors describe the graviton, <Kalb–Ramond field> and <dilaton>.