The modified cohomological crepant resolution conjecture with a flat gerbe

Let

be a Gorenstein orbifold, let $Y$ be a crepant resolution, and let $Q_1,,Q_r$ be the quantum parameters, with $s$ indexing the nonexceptional parameters. A **flat gerbe** on $Y$ determines a

-twisted small quantum product.

Modified cohomological crepant resolution conjecture. There is a flat gerbe

on $Y$ such that the Chen–Ruan product on $H^\bullet_{\mathrm{CR}}(\mathcal{X};\mathbb{C})$ can be obtained from the

-twisted small quantum product of $Y$ by analytic continuation in $Q_{s+1},\ldots,Q_r$, if necessary, followed by

$$Q_i=\begin{cases}0&1\leq i\leq s,\\1&s<i\leq r.\end{cases}$$

The source explains that this formulation incorporates the flat gerbe predicted by the preceding conjectures and removes the shift in the exceptional parameters.