In this paper we show that the two-point function for the three-loop chiral superstring measure ansatz proposed by Cacciatori, Dalla Piazza, and van Geemen [2] vanishes. Our proof uses the reformulation of the ansatz given in [8], theta functions, and specifically the theory of the Γ00 linear system, introduced by van Geemen and van der Geer [6], on Jacobians. At the two-loop level, where the amplitudes were computed by D'Hoker and Phong [11-14, 17, 18], we give a new proof of the vanishing of the two-point function (which was proven by them). We also discuss the possible approaches to proving the vanishing of the two-point function for the proposed ansatz in higher genera [3, 8, 25]. © 2009 Springer-Verlag.
The vanishing of two-point functions for three-loop superstring scattering amplitudes / Samuel, Grushevsky; SALVATI MANNI, Riccardo. - In: COMMUNICATIONS IN MATHEMATICAL PHYSICS. - ISSN 0010-3616. - STAMPA. - 294:2(2010), pp. 343-352. [10.1007/s00220-009-0967-1]
The vanishing of two-point functions for three-loop superstring scattering amplitudes
SALVATI MANNI, Riccardo
2010
Abstract
In this paper we show that the two-point function for the three-loop chiral superstring measure ansatz proposed by Cacciatori, Dalla Piazza, and van Geemen [2] vanishes. Our proof uses the reformulation of the ansatz given in [8], theta functions, and specifically the theory of the Γ00 linear system, introduced by van Geemen and van der Geer [6], on Jacobians. At the two-loop level, where the amplitudes were computed by D'Hoker and Phong [11-14, 17, 18], we give a new proof of the vanishing of the two-point function (which was proven by them). We also discuss the possible approaches to proving the vanishing of the two-point function for the proposed ansatz in higher genera [3, 8, 25]. © 2009 Springer-Verlag.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.