Partition Functions of Matrix Models as the First Special Functions of String Theory. II. Kontsevich Model - High Energy Physics - TheoryReport as inadecuate




Partition Functions of Matrix Models as the First Special Functions of String Theory. II. Kontsevich Model - High Energy Physics - Theory - Download this document for free, or read online. Document in PDF available to download.

Abstract: In arXiv:hep-th-0310113 we started a program of creating a reference-book onmatrix-model tau-functions, the new generation of special functions, which aregoing to play an important role in string theory calculations.
The main focusof that paper was on the one-matrix Hermitian model tau-functions.
The presentpaper is devoted to a direct counterpart for the Kontsevich and GeneralizedKontsevich Model GKM tau-functions.
We mostly focus on calculating resolvents=loop operator averages in the Kontsevich model, with a special emphasis onits simplest Gaussian phase, where exists a surprising integral formula, andthe expressions for the resolvents in the genus zero and one are especiallysimple in particular, we generalize the known genus zero result to genus one.We also discuss various features of generic phases of the Kontsevich model, inparticular, a counterpart of the unambiguous Gaussian solution in the genericcase, the solution called Dijkgraaf-Vafa DV solution.
Further, we extend theresults to the GKM and, in particular, discuss the p-q duality in terms ofresolvents and corresponding Riemann surfaces in the example of dualitiesbetween 2,3 and 3,2 models.



Author: A.Alexandrov, A.Mironov, A.Morozov, P.Putrov

Source: https://arxiv.org/



DOWNLOAD PDF




Related documents