The orbifold Virasoro constraints

Let $\mathcal{X}$ be a compact orbifold, let $\mathcal{D}_\mathcal{X}$ denote its total descendant Gromov–Witten potential, and let $\mathcal{L}_m$ be the Virasoro operators defined from the orbifold cohomological data. Virasoro constraints. The total descendant potential satisfies

$$\mathcal{L}_m\mathcal{D}_\mathcal{X}=0,\qquad m\geq -1.$$

The case $m=-1$ is the string equation, and the degree-zero constraint for $m=0$ follows from the virtual dimension, divisor, and dilaton equations. The full system is the orbifold extension of Givental's Virasoro constraints and remains conjectural in general.