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Matrix model calculations beyond the spherical limit. (English) Zbl 1043.81636
Nucl. Phys. B 404, No. 1-2, 127-172 (1993); erratum ibid. 449, No. 3, 681 (1995).
Summary: We propose an improved iterative scheme for calculating higher genus contributions to the multi-loop (or multi-point) correlators and the partition function of the hermitian one matrix model. We present explicit results up to genus two. We develop a version which gives directly the result in the double scaling limit and present explicit results up to genus four. Using the latter version we prove that the hermitian and the complex matrix model are equivalent in the double scaling limit and that in this limit they are both equivalent to the Kontsevich model. We discuss how our results away from the double scaling limit are related to the structure of moduli space.

MSC:
81T27 Continuum limits in quantum field theory
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
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