Multiloop Amplitudes and Vanishing Theorems using the Pure Spinor Formalism for the Superstring

2004/06/30 by Nathan Berkovits · 176 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #BRST quantization #Black Holes and Theoretical Physics #Conjecture #Covariant transformation #Formalism (music) #Homotopy and Cohomology in Algebraic Topology #Massless particle #Pure spinor #Spinor #Superstring theory #Supersymmetry #hep-th

paper · pdf · doi:10.1088/1126-6708/2004/09/047

published in Journal of High Energy Physics 2004(09), 047 (Springer Nature) · 45 pages harvmac tex, added minor clarifications

arxiv created 2004/09/22 · openalex publication_date 2004/09/22 · arxiv updated 2010/04/06 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

A ten-dimensional super-Poincare covariant formalism for the superstring was recently developed which involves a BRST operator constructed from superspace matter variables and a pure spinor ghost variable. A super-Poincare covariant prescription was defined for computing tree amplitudes and was shown to coincide with the standard RNS prescription. In this paper, picture-changing operators are used to define functional integration over the pure spinor ghosts and to construct a suitable b ghost. A super-Poincare covariant prescription is then given for the computation of N-point multiloop amplitudes. One can easily prove that massless N-point multiloop amplitudes vanish for N<4, confirming the perturbative finiteness of superstring theory. One can also prove the Type IIB S-duality conjecture that R⁴ terms in the effective action receive no perturbative contributions above one loop.

Citations

• The heterotic Green-Schwarz superstring on an N = (2,0) super world-sheet
• Effects of D-instantons
• Computing theR4term at two Superstring Loops
• Two-loop superstrings in hyperelliptic language III: the four-particle amplitude
• The geometry of string perturbation theory
• Two-loop superstrings in hyperelliptic language II: the cosmological constant and the non-renormalization theorem
• Two-loop superstrings IV
• Two-loop superstrings.

Cited by

• Superstring amplitudes meet surfaceology
• The one-loop open superstring massless five-point amplitude with the non-minimal pure spinor formalism
• Non-linear gauge transformations in D = 10 SYM theory and the BCJ duality
• On the absence of BPS preonic solutions in IIA and IIB supergravities
• Comments on BRST quantization of strings
• Super-Quantum Mechanics in the Integral Form Formalism
• The b ghost of the pure spinor formalism is nilpotent
• The structure of n-point one-loop open superstring amplitudes
• Loop amplitudes in maximal supergravity with manifest supersymmetry
• Four-point one-loop amplitude computation in the pure spinor formalism
• Čech and de Rham cohomology of integral forms
• The D10R4 term in type IIB string theory