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Perturbed generalized multicritical one-matrix models

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arxiv 1712.03879 v1 pith:2VUOQHWY submitted 2017-12-11 hep-th math-phmath.MP

J. Ambjorn , L. Chekhov , Y. Makeenko This is my paper · ORCID
classification hep-thmath-phmath.MP
keywords modelgeneralizedmulticriticalkazakovone-matrixperturbationsperturbedpotential
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abstract

We study perturbations around the generalized Kazakov multicritical one-matrix model. The multicritical matrix model has a potential where the coefficients of $z^n$ only fall off as a power $1/n^{s+1}$. This implies that the potential and its derivatives have a cut along the real axis, leading to technical problems when one performs perturbations away from the generalized Kazakov model. Nevertheless it is possible to relate the perturbed partition function to the tau-function of a KdV hierarchy and solve the model by a genus expansion in the double scaling limit.

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    In the wormhole-dominant phase of a two-dimensional matrix model, the continuum disk amplitude matches pure 2D quantum gravity, and a renormalized wormhole coupling shifts the effective bulk cosmological constant.

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