Polarization tensor (${ϵ}_{\mu \nu }$)

A closed-string polarization tensor specifies the target-spacetime tensor state multiplying $\partial X^{\mu }\bar{\partial }{X}^{\nu }{e}^{ik\cdot X}$. Its decomposition into symmetric trace-free, antisymmetric and trace parts separates the graviton, Kalb–Ramond field and dilaton polarizations.