Blobbed topological recursion from extended loop equations
We consider the N×N Hermitian matrix model with measure dμE,λ(M)=1Zexp(−λN4tr(M4))dμE,0(M), where dμE,0 is the Gaußian measure with covariance 〈MklMmn〉=δknδlmN(Ek+El) for given E1,...,EN>0. It was previously understood that this setting gives rise to two ramified coverings x,y of the Riemann sph...
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| Main Authors: | , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
June 2025
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| In: |
Journal of geometry and physics
Year: 2025, Volume: 212, Pages: 1-32 |
| DOI: | 10.1016/j.geomphys.2025.105457 |
| Online Access: | Verlag, kostenfrei, Volltext: https://doi.org/10.1016/j.geomphys.2025.105457 Verlag, kostenfrei, Volltext: https://www.sciencedirect.com/science/article/pii/S0393044025000415 
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| Author Notes: | Alexander Hock, Raimar Wulkenhaar |
MARC
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| 520 | |a We consider the N×N Hermitian matrix model with measure dμE,λ(M)=1Zexp(−λN4tr(M4))dμE,0(M), where dμE,0 is the Gaußian measure with covariance 〈MklMmn〉=δknδlmN(Ek+El) for given E1,...,EN>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 ωn(g) 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 ∞ gives global linear and quadratic loop equations for the ωn(g). These global equations provide the ωn(g) not only in the vicinity of the ramification points of x but also in the vicinity of all other poles located at opposite diagonals zi+zj=0 and at zi=0. We deduce a recursion kernel representation valid at least for g≤1. | ||
| 650 | 4 | |a (Blobbed) topological recursion | |
| 650 | 4 | |a Dyson-Schwinger equations | |
| 650 | 4 | |a Enumerative geometry | |
| 650 | 4 | |a Exactly solvable models | |
| 650 | 4 | |a Matrix models | |
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