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A Laplacian to compute intersection numbers on ℳ ¯ g , n \overline{\mathcal{M}}_{g,n} and correlation functions in NCQFT
Original
H. Grosse, A. Hock, and R. Wulkenhaar · 1903
Earlier work this paper cites.
Solution of all quartic matrix models
Original
H. Grosse, A. Hock, and R. Wulkenhaar · 1906
Earlier work this paper cites.
Self-dual noncommutative ϕ 4 \phi^{4} -theory in four dimensions is a non-perturbatively solvable and non-trivial quantum field theory
Original
H. Grosse and R. Wulkenhaar · 1906
Earlier work this paper cites.
An algebraic approach to a quartic analogue of the Kontsevich model
Original
J. Schürmann and R. Wulkenhaar · 1912
Earlier work this paper cites.
Two-dimensional gravity and intersection theory on moduli space
E. Witten · 1990
Earlier work this paper cites.
Properties of Hermitean matrix models in an external field
Yu. Makeenko and G. W. Semenoff · 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.
Large N expansion of the 2 matrix model
B. Eynard · 2003
Earlier work this paper cites.
Topological expansion for the 1-hermitian matrix model correlation functions
B. Eynard · 2004
Earlier work this paper cites.
Matrix Field Theory
Original
A. Hock · 2005
Earlier work this paper cites.
Free energy topological expansion for the 2-matrix model
L. Chekhov, B. Eynard, and N. Orantin · 2006
Earlier work this paper cites.
Invariants of algebraic curves and topological expansion
B. Eynard and N. Orantin · 2007
Earlier work this paper cites.

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2023

Blobbed topological recursion from extended loop equations

Hock, Alexander, Wulkenhaar, Raimar

Understand

We consider the $N\times N$ Hermitian matrix model with measure $d\mu_{E,\lambda}(M)=\frac{1}{Z} \exp(-\frac{\lambda N}{4} \mathrm{tr}(M^4)) d\mu_{E,0}(M)$, where $d\mu_{E,0}$ is the Gaussian measure with covariance $\langle M_{kl}M_{mn}\rangle=\frac{\delta_{kn}\delta_{lm}}{N(E_k+E_l)}$ for given $E_1,...,E_N>0$.

It was previously understood that this setting gives rise to two ramified coverings $x,y$ of the Riemann sphere strongly tied by $y(z)=-x(-z)$ and a family $\omega^{(g)}_{n}$ of meromorphic differentials conjectured to obey blobbed topological recursion due to Borot and Shadrin.
We develop a new approach to this problem via a system of six meromorphic functions which satisfy extended loop equations.
Two of these functions are symmetric in the preimages of $x$ and can be determined from their consistency relations.

Built on

A Laplacian to compute intersection numbers on ℳ ¯ g , n \overline{\mathcal{M}}_{g,n} and correlation functions in NCQFT
Original
H. Grosse, A. Hock, and R. Wulkenhaar · 1903
Earlier work this paper cites.
Solution of all quartic matrix models
Original
H. Grosse, A. Hock, and R. Wulkenhaar · 1906
Earlier work this paper cites.
Self-dual noncommutative ϕ 4 \phi^{4} -theory in four dimensions is a non-perturbatively solvable and non-trivial quantum field theory
Original
H. Grosse and R. Wulkenhaar · 1906
Earlier work this paper cites.
An algebraic approach to a quartic analogue of the Kontsevich model
Original
J. Schürmann and R. Wulkenhaar · 1912
Earlier work this paper cites.
Two-dimensional gravity and intersection theory on moduli space
E. Witten · 1990
Earlier work this paper cites.
Properties of Hermitean matrix models in an external field
Yu. Makeenko and G. W. Semenoff · 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.
Large N expansion of the 2 matrix model
B. Eynard · 2003
Earlier work this paper cites.
Topological expansion for the 1-hermitian matrix model correlation functions
B. Eynard · 2004
Earlier work this paper cites.
Matrix Field Theory
Original
A. Hock · 2005
Earlier work this paper cites.
Free energy topological expansion for the 2-matrix model
L. Chekhov, B. Eynard, and N. Orantin · 2006
Earlier work this paper cites.
Invariants of algebraic curves and topological expansion
B. Eynard and N. Orantin · 2007
Earlier work this paper cites.