= Infinitesimal worldsheet modulus
{title2=$h^{ab}t_{ab}=0,\quad\nabla^at_{ab}=0$}
= Infinitesimal worldsheet moduli
{synonym}
After quotienting infinitesimal <worldsheet diffeomorphisms> and <Weyl transformations>, choose a metric variation orthogonal to the gauge directions. Orthogonality to Weyl scaling makes its trace zero; the <formal adjoint of the worldsheet conformal Killing operator> makes its divergence zero. These are transverse-traceless variations of the two-dimensional metric. In a local conformal complex coordinate, their nonzero components satisfy $\partial_{\bar z}t_{zz}=0$ and its conjugate, linking them to <holomorphic quadratic differentials>.
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