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From Kontsevich-Witten to linear Hodge integrals via Virasoro operators

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We give a proof of Alexandrov's conjecture on a formula connecting the Kontsevich-Witten and Hodge tau-functions using only the Virasoro operators. This formula has been confirmed up to an unknown… Click to show full abstract

We give a proof of Alexandrov's conjecture on a formula connecting the Kontsevich-Witten and Hodge tau-functions using only the Virasoro operators. This formula has been confirmed up to an unknown constant factor. In this paper, we show that this factor is indeed equal to one by investigating series expansions for the Lambert W function on different points.

Keywords: linear hodge; witten linear; virasoro operators; kontsevich witten; hodge integrals

Journal Title: Journal of Mathematical Physics
Year Published: 2018

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