Combining certain identities for modular forms due to lgusa with Schottky-Jung relations, we study the cosmological constant for the recently proposed ansatz for the chiral superstring measure in genus 5. The vanishing of this cosmological constant turns out to be equivalent to the long-conjectured vanishing of a certain explicit modular form of genus 5 on the moduli of curves M-5, and we disprove this conjecture, thus showing that the cosmological constant for the proposed ansatz does not vanish identically. We exhibit an easy modification of the genus 5 ansatz satisfying factorization constraints and yielding a vanishing cosmological constant. We also give an expression for the cosmological constant for the proposed ansatz that should hold for any genus if certain generalized Schottky-Jung identities hold.

THE SUPERSTRING COSMOLOGICAL CONSTANT AND THE SCHOTTKY FORM IN GENUS 5 / S., Grushevsky; SALVATI MANNI, Riccardo. - In: AMERICAN JOURNAL OF MATHEMATICS. - ISSN 0002-9327. - STAMPA. - 133:(2011), pp. 1007-1027.

THE SUPERSTRING COSMOLOGICAL CONSTANT AND THE SCHOTTKY FORM IN GENUS 5

SALVATI MANNI, Riccardo
2011

Abstract

Combining certain identities for modular forms due to lgusa with Schottky-Jung relations, we study the cosmological constant for the recently proposed ansatz for the chiral superstring measure in genus 5. The vanishing of this cosmological constant turns out to be equivalent to the long-conjectured vanishing of a certain explicit modular form of genus 5 on the moduli of curves M-5, and we disprove this conjecture, thus showing that the cosmological constant for the proposed ansatz does not vanish identically. We exhibit an easy modification of the genus 5 ansatz satisfying factorization constraints and yielding a vanishing cosmological constant. We also give an expression for the cosmological constant for the proposed ansatz that should hold for any genus if certain generalized Schottky-Jung identities hold.
2011
01 Pubblicazione su rivista::01a Articolo in rivista
THE SUPERSTRING COSMOLOGICAL CONSTANT AND THE SCHOTTKY FORM IN GENUS 5 / S., Grushevsky; SALVATI MANNI, Riccardo. - In: AMERICAN JOURNAL OF MATHEMATICS. - ISSN 0002-9327. - STAMPA. - 133:(2011), pp. 1007-1027.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/19088
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