Integrating simple genus two string invariants over moduli space

A bstract We consider an Sp(4 , ℤ) invariant expression involving two factors of the Kawazumi-Zhang (KZ) invariant each of which is a modular graph with one link, and four derivatives on the moduli space of genus two Riemann surfaces. Manipulating it, we show that the integral over moduli space of a...

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Veröffentlicht in:The journal of high energy physics 2021-03, Vol.2021 (3), p.1-26, Article 158
1. Verfasser: Basu, Anirban
Format: Artikel
Sprache:eng
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Zusammenfassung:A bstract We consider an Sp(4 , ℤ) invariant expression involving two factors of the Kawazumi-Zhang (KZ) invariant each of which is a modular graph with one link, and four derivatives on the moduli space of genus two Riemann surfaces. Manipulating it, we show that the integral over moduli space of a linear combination of a modular graph with two links and the square of the KZ invariant reduces to a boundary integral. We also consider an Sp(4 , ℤ) invariant expression involving three factors of the KZ invariant and six derivatives on moduli space, from which we deduce that the integral over moduli space of a modular graph with three links reduces to a boundary integral. In both cases, the boundary term is completely determined by the KZ invariant. We show that both the integrals vanish.
ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP03(2021)158