Do we need the $W^{(n>3)}$ constraints to solve the $(1,q)$ models coupled to 2D gravity?

Details Do we need the $W^{(n>3)}$ constraints to solve the $(1,q)$ models coupled to 2D gravity? Do we need the $W^{(n>3)}$ constraints to solve the $(1,q)$ models coupled to 2D gravity?

1993-07-09

arxiv.org/abs/hep-th/9307073v1

Nucl.Phys. B414 (1994) 329-347

Physics

High Energy Physics

High Energy Physics - Theory

26 pages

Scientific paper

10.1016/0550-3213(94)90433-2

We prove that all the correlation functions in the $(1,q)$ models are calculable using only the Virasoro and the $W^{(3)}$ constraints. This result is based on the invariance of correlators with respect to an interchange of the order of the operators they contain. In terms of the topological recursion relations, it means that only two and three contacts and the corresponding degenerations of the underlying surfaces are relevant. An algorithm to compute correlators for any $q$ and at any genus is presented and demonstrated through some examples. On route to these results, some interesting polynomial identities, which are generalizations of Abel's identity, were discovered. }

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