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- W4315706718 abstract "We consider the $Ntimes N$ Hermitian matrix model with measure $dmu_{E,lambda}(M)=frac{1}{Z} exp(-frac{lambda N}{4} mathrm{tr}(M^4)) dmu_{E,0}(M)$, where $dmu_{E,0}$ 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. An expansion at $infty$ gives global linear and quadratic loop equations for the $omega^{(g)}_{n}$. These global equations provide the $omega^{(g)}_{n}$ not only in the vicinity of the ramification points of $x$ but also in the vicinity of all other poles located at opposite diagonals $z_i+z_j=0$ and at $z_i=0$. We deduce a recursion kernel representation valid at least for $gleq 1$." @default.
- W4315706718 created "2023-01-12" @default.
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- W4315706718 date "2023-01-10" @default.
- W4315706718 modified "2023-09-25" @default.
- W4315706718 title "Blobbed topological recursion from extended loop equations" @default.
- W4315706718 doi "https://doi.org/10.48550/arxiv.2301.04068" @default.
- W4315706718 hasPublicationYear "2023" @default.
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