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This article is cited in 5 scientific papers (total in 5 papers)
Topological recursion for Gaussian means and cohomological field
theories
J. E. Andersenab, L. O. Chekhovc, P. Norburyd, R. C. Pennereb a Center for Quantum Geometry of Moduli Spaces, Århus University, Denmark
b California Institute of Technology, Pasadena, USA
c Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
d University of Melbourne, Melbourne, Australia
e Institut des Hautes Études Scientifiques, Bures-sur-Yvette, France
Abstract:
We introduce explicit relations between genus-filtrated $s$-loop means of the Gaussian matrix model and terms of the genus expansion of the Kontsevich–Penner matrix model (KPMM{), which is the generating function for volumes of discretized (openm) moduli spaces $M_{g,s}^\mathrm{disc}$ (discrete volumes). Using these relations, we express Gaussian means in all orders of the genus expansion as polynomials in special times weighted by ancestor invariants of an underlying cohomological field theory. We translate the topological recursion of the Gaussian model into recurrence relations for the coefficients of this expansion, which allows proving that they are integers and positive. We find the coefficients in the first subleading order for $\\mathcal M_{g,1}$ for all $g$ in three ways: using the refined Harer–Zagier recursion, using the Givental-type decomposition of the KPMM, and counting diagrams explicitly.
Keywords:
chord diagram, Givental decomposition, Kontsevich–Penner matrix model, discrete volume, moduli space, Deligne–Mumford compactification.
Received: 15.04.2015
Citation:
J. E. Andersen, L. O. Chekhov, P. Norbury, R. C. Penner, “Topological recursion for Gaussian means and cohomological field
theories”, TMF, 185:3 (2015), 371–409; Theoret. and Math. Phys., 185:3 (2015), 1685–1717
Linking options:
https://www.mathnet.ru/eng/tmf8951https://doi.org/10.4213/tmf8951 https://www.mathnet.ru/eng/tmf/v185/i3/p371
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