Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2004-08-27
Nucl.Phys. B704 (2005) 181-207
Physics
High Energy Physics
High Energy Physics - Theory
34 pages, 2 eps figures, LaTex; typos corrected (including title); more typos fixed, including those in Eqs.(72) and (132)
Scientific paper
10.1016/j.nuclphysb.2004.10.020
We point out that insertions of matrix fields in (connected amputated) amplitudes of (generalized) Kontsevich models are given by covariant derivatives with respect to the Kontsevich moduli. This implies that correlators are sections of symmetric products of the (holomorphic) tangent bundle on the (complexified) moduli space of FZZT Liouville branes. We discuss the relation of Kontsevich parametrization of moduli space with that provided by either the (p,1) or the (1,p) boundary conformal field theories. It turns out that the Kontsevich connection captures the contribution of contact terms to open string amplitudes of boundary cosmological constant operators in the (1,p) minimal string models. The curvature of the connection is of type (1,1) and has delta-function singularities at the points in moduli space where Kontsevich kinetic term vanishes. We also outline the extention of our formalism to the c=1 string at self-dual radius and discuss the problems that have to be understood to reconciliate first and second quantized approaches in this case.
Giusto Stefano
Imbimbo Camillo
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