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In this paper, we formulate and present ample evidence towards the conjecturethat the partition function (i.e. the exponential of the generating series ofintersection numbers with monomials in psi classes) of the Pixton class on themoduli space of stable curves is the topological tau function of thenoncommutative KdV hierarchy, which we introduced in a previous work. Thespecialization of this conjecture to the top degree part of Pixton's classstates that the partition function of the double ramification cycle is the taufunction of the dispersionless limit of this hierarchy. In fact, we prove thatthis conjecture follows from the Double Ramification/Dubrovin--Zhangequivalence conjecture. We also provide several independent computationalchecks in support of it.

A generalization of Witten's conjecture for the Pixton class and the noncommutative KdV hierarchy