The Virasoro conjecture for admissible Landau–Ginzburg A-model pairs

Let $(W,G)$ be an admissible Landau–Ginzburg pair, and let $\mathcal{A}^{\clubsuit}_{W,G}$ denote its total ancestor potential in FJRW, Polishchuk–Vaintrob, or Kiem–Li theory. Let $L_k$ be the Virasoro operators defined in the paper. Virasoro conjecture for admissible LG A-model pairs. For every admissible LG pair $(W,G)$, the total ancestor potential satisfies

$$L_k\mathcal{A}^{\clubsuit}_{W,G}=0,\qquad \text{for all }k\geq -1.$$

This extends the Virasoro constraints from semisimple Frobenius manifolds to admissible Landau–Ginzburg theories. The conjecture is established in several special cases treated in the paper, but is open for general admissible pairs.