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We prove a formula for the genus one free energy $\mathcal{F}^{(1)}$ of the quartic Kontsevich model for arbitrary ramification by working out a boundary creation operator for blobbed topological recursion.
Solution of all quartic matrix models
H. Grosse, A. Hock, and R. Wulkenhaar · 1906
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An algebraic approach to a quartic analogue of the Kontsevich model
J. Schürmann and R. Wulkenhaar · 1912
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A Census of Planar Maps
W. Tutte · 1963
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A Planar Diagram Theory for Strong Interactions
G. ’t Hooft · 1974
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Planar Diagrams
E. Brezin, C. Itzykson, G. Parisi, and J. B. Zuber · 1978
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The Enumeration of Maps on the Torus and the Projective Plane
E. Bender and E. R. Canfield · 1988
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Checkered surfaces and complex matrices
T. R. Morris · 1991
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Intersection theory on the moduli space of curves and the matrix Airy function
M. Kontsevich · 1992
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Large N expansion of the 2-matrix model
B. Eynard · 2003
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Bergmann tau-function on Hurwitz spaces and its applications
A. Kokotov and D. Korotkin · 2003
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Matrix integrals and the generation and counting of virtual tangles and links
P. Zinn-Justin and J. B. Zuber · 2004
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1 N 2 \frac{1}{N^{2}} correction to free energy in hermitian two-matrix model
B. Eynard, A. Kokotov, and D. Korotkin · 2005
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2-matrix versus complex matrix model, integrals over the unitary group as triangular integrals
B. Eynard and A. Ferrer · 2006
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Invariants of algebraic curves and topological expansion
B. Eynard and N. Orantin · 2007
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Blobbed topological recursion of the quartic Kontsevich model I: Loop equations and conjectures
J. Branahl, A. Hock, and R. Wulkenhaar · 2008
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Progress in solving a noncommutative quantum field theory in four dimensions
Simple recurrence formulas to count maps on orientable surfaces
S. Carrell and G. Chapuy · 2014
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Abstract loop equations, topological recursion and new applications
G. Borot, B. Eynard, and N. Orantin · 2015
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Counting Surfaces
B. Eynard · 2016
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Blobbed topological recursion: properties and applications
G. Borot and S. Shadrin · 2017
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Simple maps, Hurwitz numbers, and Topological Recursion
G. Borot and E. Garcia-Failde · 2020
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H. Grosse and R. Wulkenhaar · 2009
Cited alongside, same era.
Enumeration of maps with self avoiding loops and the O(n) model on random lattices of all topologies
G. Borot and B. Eynard · 2011
Cited alongside, same era.
Perturbative and geometric analysis of the quartic Kontsevich model
J. Branahl, A. Hock, and R. Wulkenhaar · 2012
Cited alongside, same era.
Formal multidimensional integrals, stuffed maps, and topological recursion
G. Borot · 2014
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G. Borot, S. Charbonnier, and E. Garcia-Failde · 2021
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From scalar fields on quantum spaces to blobbed topological recursion
J. Branahl, H. Grosse, A. Hock, and R. Wulkenhaar · 2021
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A new spin on Hurwitz theory and ELSV via theta characteristics
A. Giacchetto, R. Kramer and D. Lewanski · 2021
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Blobbed topological recursion of the quartic Kontsevich model II: Genus=0
A. Hock and R. Wulkenhaar · 2021
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