Complete N-Point Superstring Disk Amplitude II. Amplitude and Hypergeometric Function Structure

Abstract

Using the pure spinor formalism in part I [1] we compute the complete tree-level amplitude of N massless open strings and find a striking simple and compact form in terms of minimal building blocks: the full N-point amplitude is expressed by a sum over (N-3)! Yang-Mills partial subamplitudes each multiplying a multiple Gaussian hypergeometric function. While the former capture the space-time kinematics of the amplitude the latter encode the string effects. This result disguises a lot of structure linking aspects of gauge amplitudes as color and kinematics with properties of generalized Euler integrals. In this part II the structure of the multiple hypergeometric functions is analyzed in detail: their relations to monodromy equations, their minimal basis structure, and methods to determine their poles and transcendentality properties are proposed. Finally, a Groebner basis analysis provides independent sets of rational functions in the Euler integrals.

68 pages, harvmac TeX

References in corpus (10)

• New Relations for Gauge-Theory Amplitudes
• Minimal Basis for Gauge Theory Amplitudes
• E7(7) constraints on counterterms in N=8 supergravity
• Multi-Gluon Scattering in Open Superstring Theory
• All tree-level amplitudes in massless QCD
• Stringy KLT relations, global symmetries, and E_7(7) violation
• Amplitude for N-Gluon Superstring Scattering
• Supersymmetry Relations and MHV Amplitudes in Superstring Theory
• Complete Six-Gluon Disk Amplitude in Superstring Theory
• PSS: A FORM Program to Evaluate Pure Spinor Superspace Expressions