Abstract
We demonstrate an equivalence between two integrable flows defined in a polynomial ring quotiented by an ideal generated by a polynomial. This duality of integrable systems allows us to systematically exploit the Korteweg-de Vries hierarchy and its tau-function to propose amplitudes for non-compact topological gravity on Riemann surfaces of arbitrary genus. We thus quantize topological gravity coupled to non-compact topologica matter and demonstrate that this phase of topological gravity at N = 2 matter central charge larger than three is equivalent to the phase with matter of central charge smaller than three.
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Ashok, S.K., Troost, J. A duality in two-dimensional gravity. J. High Energ. Phys. 2019, 111 (2019). https://doi.org/10.1007/JHEP05(2019)111
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DOI: https://doi.org/10.1007/JHEP05(2019)111