Loop equations and integrable hierarchies for special cubic Hodge integrals

Abstract: By using the Virasoro constraints we derive the loop equations for the cubic Hodge partition function with three parameters p,q,r satisfying the Calabi-Yau condition pq + qr + rp = 0. We then show that the Hodge integrable hierarchy associated to the special cubic Hodge integrals is normal Miura equivalent to the fractional Volterra hierarchy. In the procedure of the proof, a particular tau-function for the fractional Volterra hierarchy is constructed, which we call the topological tau-function. Finally, when one of the three parameters p,q,r is equal to 1, we prove a certain gap condition for the logarithm of the topological tau-function. The talk is based on joint works with Si-Qi Liu, Youjin Zhang and Chunhui Zhou.

HEP - theorymathematical physicsalgebraic geometrycombinatoricsexactly solvable and integrable systems

Audience: researchers in the discipline

IBS-CGP Mathematical Physics Seminar

Series comments: Registration is required at cgp.ibs.re.kr/activities/talkregistration