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Planar diagrams
É. Brézin, C. Itzykson, G. Parisi, and J.-B. Zuber · 1978
Earlier work this paper cites.
The Euler characteristics of the moduli space of curves
J. Harer and D. Zagier · 1986
Earlier work this paper cites.
Two dimensional gravity and intersection theory on moduli space
E. Witten · 1991
Earlier work this paper cites.
Intersection theory on the moduli space of curves and the matrix Airy function
M. Kontsevich · 1992
Earlier work this paper cites.
Gromov-Witten invariants and quantization of quadratic Hamiltonians
A.B. Givental · 2001
Earlier work this paper cites.
Invariants of algebraic curves and topological expansion
B. Eynard and N. Orantin · 2007
Earlier work this paper cites.
Weil-Petersson volume of moduli spaces, Mirzakhani’s recursion and matrix models
Original
B. Eynard and N. Orantin · 2007
Earlier work this paper cites.
Topological expansion of mixed correlations in the hermitian 2 2 matrix model and x − y x-y symmetry of the F g F_{g} invariants
Original
B. Eynard and N. Orantin · 2008
Earlier work this paper cites.
Remodeling the B-model
Original
V. Bouchard, A. Klemm, M. Mariño, and S. Pasquetti · 2009
Earlier work this paper cites.

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2015

Borot, Gaëtan, Shadrin, Sergey

We study the set of solutions $(\omega_{g,n})_{g \geq 0,n \geq 1}$ of abstract loop equations.

We prove that $\omega_{g,n}$ is determined by its purely holomorphic part: this results in a decomposition that we call "blobbed topological recursion".
This is a generalization of the theory of the topological recursion, in which the initial data $(\omega_{0,1},\omega_{0,2})$ is enriched by non-zero symmetric holomorphic forms in $n$ variables $(\phi_{g,n})_{2g - 2 + n > 0}$.
In particular, we establish for any solution of abstract loop equations: (1) a graphical representation of $\omega_{g,n}$ in terms of $\phi_{g,n}$; (2) a graphical representation of $\omega_{g,n}$ in terms of intersection numbers on the moduli space of curves; (3) variational formulae under infinitesimal transformation of $\phi_{g,n}$ ; (4) a definition for the free energies $\omega_{g,0} = F_g$ respecting the variational formulae.

Planar diagrams
É. Brézin, C. Itzykson, G. Parisi, and J.-B. Zuber · 1978
Earlier work this paper cites.
The Euler characteristics of the moduli space of curves
J. Harer and D. Zagier · 1986
Earlier work this paper cites.
Two dimensional gravity and intersection theory on moduli space
E. Witten · 1991
Earlier work this paper cites.
Intersection theory on the moduli space of curves and the matrix Airy function
M. Kontsevich · 1992
Earlier work this paper cites.
Gromov-Witten invariants and quantization of quadratic Hamiltonians
A.B. Givental · 2001
Earlier work this paper cites.
Invariants of algebraic curves and topological expansion
B. Eynard and N. Orantin · 2007
Earlier work this paper cites.
Weil-Petersson volume of moduli spaces, Mirzakhani’s recursion and matrix models
Original
B. Eynard and N. Orantin · 2007
Earlier work this paper cites.
Topological expansion of mixed correlations in the hermitian 2 2 matrix model and x − y x-y symmetry of the F g F_{g} invariants
Original
B. Eynard and N. Orantin · 2008
Earlier work this paper cites.
Remodeling the B-model
Original
V. Bouchard, A. Klemm, M. Mariño, and S. Pasquetti · 2009
Earlier work this paper cites.