# Abstract loop equations, topological recursion, and applications

@article{Borot2013AbstractLE, title={Abstract loop equations, topological recursion, and applications}, author={Gaetan Borot and Bertrand Eynard and Nicolas Orantin}, journal={arXiv: Mathematical Physics}, year={2013} }

We formulate a notion of abstract loop equations, and show that their solution is provided by a topological recursion under some assumptions, in particular the result takes a universal form. The Schwinger-Dyson equation of the one and two hermitian matrix models, and of the O(n) model appear as special cases. We study applications to repulsive particles systems, and explain how our notion of loop equations are related to Virasoro constraints. Then, as a special case, we study in detail…

## 81 Citations

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