Superstring measure and non-renormalization of the three-point amplitude
arXiv:0806.4370 · doi:10.1016/j.nuclphysb.2008.08.011
Abstract
We show that a recently conjectured expression for the superstring three-point amplitude, in the framework of the Cacciatori, Dalla Piazza, van Geemen - Grushevsky ansatz for the chiral measure, fails to vanish at three-loop, in contrast with expectations from non-renormalization theorems. Based on analogous two-loop computations, we discuss the possibility of a non-trivial correction to the amplitude and propose a natural candidate for such a contribution. Thanks to a new remarkable identity, it is reasonable to expect that the corrected three-point amplitude vanishes at three-loop, recovering the agreement with non-renormalization theorems.
14 pages; minor corrections, some comments added. Accepted for publication in Nucl.Phys.B
References in corpus (17)
- Two-Loop Superstrings VI: Non-Renormalization Theorems and the 4-Point Function
- Two-Loop Superstrings I, Main Formulas
- Two-loop superstrings and S-duality
- Two-Loop Superstrings II, The Chiral Measure on Moduli Space
- Two-Loop Superstrings III, Slice Independence and Absence of Ambiguities
- Two-Loop Superstrings V: Gauge Slice Independence of the N-Point Function
- Modular Forms and Three Loop Superstring Amplitudes
- Asyzygies, modular forms, and the superstring measure II
- Superstring scattering amplitudes in higher genus
- Higher genus superstring amplitudes from the geometry of moduli spaces
- Asyzygies, modular forms, and the superstring measure I
- Remarks on Superstring amplitudes in higher genus
- Two-Loop Superstrings VII, Cohomology of Chiral Amplitudes
- The vanishing of two-point functions for three-loop superstring scattering amplitudes
- NSR measures on hyperelliptic locus and non-renormalization of 1,2,3-point functions
- Siegel modular forms and finite symplectic groups
- Complex Geometry and Supergeometry
Cited by in corpus (19)
- Analytical Solutions of Open String Field Theory
- Superstring loop amplitudes from the field theory limit
- The vanishing of two-point functions for three-loop superstring scattering amplitudes
- Getting superstring amplitudes by degenerating Riemann surfaces
- Lattice Theta Constants vs Riemann Theta Constants and NSR Superstring Measures
- Higher genus partition functions of meromorphic conformal field theories
- One-Dimensional Super Calabi-Yau Manifolds and their Mirrors
- More on superstring chiral measures
- Topics in Two-Loop Superstring Perturbation Theory
- Extending the Belavin-Knizhnik "wonderful formula" by the characterization of the Jacobian
- Energy Quantisation and Time Parameterisation
- NSR superstring measures in genus 5
- The superstring cosmological constant and the Schottky form in genus 5
- Modular Invariant Regularization of String Determinants and the Serre GAGA Principle
- Non-analytic terms of string amplitudes from partial waves
- Finite Strings From Non-Chiral Mumford Forms
- Uniformization, Unipotent Flows and the Riemann Hypothesis
- Eluding SUSY at every genus on stable closed string vacua
- Singular Spin Structures and Superstrings