Abstract
To any flat section equation of the form \(\nabla _0\Psi =\Phi \Psi \) in a principal bundle over a Riemann surface (\(\nabla _0\) is a reference connection), we associate an infinite sequence of “correlators”, symmetric n-differentials on \(\Sigma \) that we denote \(\{W-n\}_{n \in \mathcal {N}}\). The goal of this article is to prove that these correlators are solutions to “loop equations,” the same ones satisfied by correlation functions in random matrix models, or equivalently Ward identities of Virasoro or \({\mathcal {W}}\)-symmetric CFT.
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Communicated by Boris Pioline.
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Belliard, R., Eynard, B. & Marchal, O. Loop Equations from Differential Systems on Curves. Ann. Henri Poincaré 19, 141–161 (2018). https://doi.org/10.1007/s00023-017-0622-x
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DOI: https://doi.org/10.1007/s00023-017-0622-x