Two-Loop Superstrings VII, Cohomology of Chiral Amplitudes

Abstract

The relation between superholomorphicity and holomorphicity of chiral superstring N-point amplitudes for NS bosons on a genus 2 Riemann surface is shown to be encoded in a hybrid cohomology theory, incorporating elements of both de Rham and Dolbeault cohomologies. A constructive algorithm is provided which shows that, for arbitrary N and for each fixed even spin structure, the hybrid cohomology classes of the chiral amplitudes of the N-point function on a surface of genus 2 always admit a holomorphic representative. Three key ingredients in the derivation are a classification of all kinematic invariants for the N-point function, a new type of 3-point Green's function, and a recursive construction by monodromies of certain sections of vector bundles over the moduli space of Riemann surfaces, holomorphic in all but exactly one or two insertion points.

103 pages, 2 figures

References in corpus (39)

• MHV Vertices And Tree Amplitudes In Gauge Theory
• One loop in eleven dimensions
• On-Shell Methods in Perturbative QCD
• Supersymmetry Constraints on Type IIB Supergravity
• Two-Loop Superstrings VI: Non-Renormalization Theorems and the 4-Point Function
• Two loops in eleven dimensions
• Multiloop Amplitudes and Vanishing Theorems using the Pure Spinor Formalism for the Superstring
• The low energy expansion of the one-loop type II superstring amplitude
• Equivalence of Two-Loop Superstring Amplitudes in the Pure Spinor and RNS Formalisms
• Two-Loop Superstrings I, Main Formulas
• Two-Loop Superstrings II, The Chiral Measure on Moduli Space
• Two-loop superstrings and S-duality
• Two-Loop Superstrings IV, The Cosmological Constant and Modular Forms
• Super-Poincare Covariant Two-Loop Superstring Amplitudes
• Multiloop Superstring Amplitudes from Non-Minimal Pure Spinor Formalism
• Two-Loop Superstrings III, Slice Independence and Absence of Ambiguities
• Two-Loop Superstrings V: Gauge Slice Independence of the N-Point Function
• A note on non-perturbative R^4 couplings
• The Box Graph In Superstring Theory
• Lectures on Two-Loop Superstrings
• The D^4 R^4 term in type IIB string theory on T^2 and U-duality
• Asyzygies, modular forms, and the superstring measure II
• Type IIB $R^4{H}^{4g-4}$ Conjectures
• Momentum Analyticity and Finiteness of the 1-Loop Superstring Amplitude
• Higher genus superstring amplitudes from the geometry of moduli spaces
• Construction of $R^4$ Terms in N=2 D=8 Superspace
• Asyzygies, modular forms, and the superstring measure I
• Explicit Modular Invariant Two-Loop Superstring Amplitude Relevant for R^4
• Eisenstein Series in String Theory
• Dispersion Relations in String Theory
• Two-Loop Superstrings in Hyperelliptic Language I: the Main Results
• The D^{10} R^4 term in type IIB string theory
• Two loop superstring amplitudes and S_6 representations
• Two-Loop Superstrings in Hyperelliptic Language II: the Vanishing of the Cosmological Constant and the Non-Renormalization Theorem
• Two-Loop Superstrings in Hyperelliptic Language III: the Four-Particle Amplitude
• Comments on Two-Loop Four-Particle Amplitude in Superstring Theory
• An ansatz for a non-perturbative four-graviton amplitude in type IIB superstring theory
• Recent Progress in Perturbative Quantum Field Theory
• Complex Geometry and Supergeometry

Cited by in corpus (24)

• Closed Superstring Field Theory and its Applications
• Off-shell Amplitudes in Superstring Theory
• Tropical Amplitudes
• Mass Renormalization in String Theory: General States
• Mass Renormalization in String Theory: Special States
• Gauge Invariant 1PI Effective Superstring Field Theory: Inclusion of the Ramond Sector
• Superstring measure and non-renormalization of the three-point amplitude
• Getting superstring amplitudes by degenerating Riemann surfaces
• String Perturbation Theory Around Dynamically Shifted Vacuum
• Supersymmetry Restoration in Superstring Perturbation Theory
• Two-loop superstring five-point amplitudes III, construction via the RNS formulation: even spin structures
• Lattice Theta Constants vs Riemann Theta Constants and NSR Superstring Measures
• One-Dimensional Super Calabi-Yau Manifolds and their Mirrors
• Topics in Two-Loop Superstring Perturbation Theory
• Gauge Invariant 1PI Effective Action for Superstring Field Theory
• Extending the Belavin-Knizhnik "wonderful formula" by the characterization of the Jacobian
• Cyclic products of Szegö kernels and spin structure sums I: hyper-elliptic formulation
• NSR superstring measures in genus 5
• Modular Invariant Regularization of String Determinants and the Serre GAGA Principle
• Two-loop superstring five-point amplitudes I: Construction via chiral splitting and pure spinors
• Supermoduli and PCOs at Genus Two
• Finite Strings From Non-Chiral Mumford Forms
• Hyperbolic Geometry of Superstring Perturbation Theory
• The Super Mumford Form and Sato Grassmannian