Chiral Rings and Integrable Systems for Models of Topological Gravity

Details Chiral Rings and Integrable Systems for Models of Topological Gravity Chiral Rings and Integrable Systems for Models of Topological Gravity

1994-01-25

arxiv.org/abs/hep-th/9401121v1

Physics

High Energy Physics

High Energy Physics - Theory

19p, plain tex, 1 uuencoded PostScript figure

Scientific paper

(Talk given at Strings '93, Berkeley, and at XXVII. Internationales Symposium \"uber Elementarteilchentheorie, Wendisch-Rietz, 1993) We review the superconformal properties of matter coupled to $2d$ gravity, and $W$-extensions thereof. We show in particular how the \nex2 structure provides a direct link between certain matter-gravity systems and matrix models. We also show that much, probably all, of this can be generalized to $W$-gravity, and this leads to an infinite class of new exactly solvable systems. These systems are governed by certain integrable hierarchies, which are generalizations of the usual KdV hierarchy and whose algebraic structure is given in terms of quantum cohomology rings of grassmannians.

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