Hodge–FVH correspondence for special cubic Hodge integrals
Let H(t;p,q,r;ϵ)\mathcal{H}({\bf t};p,q,r;\epsilon)H(t;p,q,r;ϵ) be the cubic Hodge free energy, let w=ϵ2∂t02H(t;p,q,r;ϵ)w=\epsilon^2\partial_{t_0}^2\mathcal{H}({\bf t};p,q,r;\epsilon)w=ϵ2∂t02H(t;p,q,r;ϵ), and let…
The Dubrovin–Yang conjecture on the special cubic Hodge hierarchy
Let p,q,re0p,q,r e 0p,q,re0 satisfy the local Calabi–Yau condition 1/p+1/q+1/r=01/p+1/q+1/r=01/p+1/q+1/r=0, with r=−pq/(p+q)r=-pq/(p+q)r=−pq/(p+q). Set sj=−(2j−2)!(p2j−1+q2j−1+r2j−1)sj=-(2j-2)!(p^{2j-1}+q^{2j-1}+r^{2j-1})sj=−(2j−2)!(p2j−1+q2j−1+r2j−1), α=p/p+q\alpha=p/\sqrt{p+q}α=p/p+q, and…