Q-graded correlator conjecture for open intersection numbers

Let τQ=eFQ\tau_Q=e^{F_Q} be the Kontsevich–Penner matrix-model partition function, and expand

FQ(t)=g,nu2g2Fg,n(Q;t).F_Q(t)=\sum_{g,n}u^{2g-2}F_{g,n}(Q;t).

For the correlators define

Wg,n(Q;z)=δ1δnFg,n(Q;t).W_{g,n}(Q;\vec z)=\delta_1\cdots\delta_nF_{g,n}(Q;t).

Q-graded correlator conjecture. These correlators are the QQ-graded correlators for open intersection numbers. The proposed grading is intended to separate contributions by boundary-component number and to provide correlators suitable for a spectral-curve formulation of topological recursion; the source presents this as conjectural and gives no resolution.

Sources & referencesView supporting material

Primary source

Brad Safnuk, “Topological recursion for open intersection numbers”, arXiv:1601.04049 (2016).

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