Multi-loop amplitudes in maximally supersymmetric pure spinor field theory

Abstract

This paper provides a more detailed background to the results of arXiv:1004.2692 concerning properties of multi-loop amplitudes in a pure spinor formulation of field theories with maximal supersymmetry. This involves the development of a first quantised field theory version of the non-minimal pure spinor formalism originally designed for describing superstring amplitudes. In addition to superspace world-line fields, the formalism involves a set of world-line ghost fields that are required for implementing BRST invariance with a composite b ghost. In particular, we show that BRST invariance requires the presence of certain contact terms. For four-point amplitudes, these are important beyond two loops. We also present an alternative proof of the "no-triangle hypothesis" and the vanishing of amplitudes with fewer than four external particles.

65 pages, 15 figures

References in corpus (53)

• New Relations for Gauge-Theory Amplitudes
• Perturbative Quantum Gravity as a Double Copy of Gauge Theory
• Super-Poincare Covariant Quantization of the Superstring
• What is the Simplest Quantum Field Theory?
• On the Relationship between Yang-Mills Theory and Gravity and its Implication for Ultraviolet Divergences
• Effects of D-instantons
• Gravity as the Square of Gauge Theory
• The Ultraviolet Behavior of N=8 Supergravity at Four Loops
• Two-Loop Four-Gluon Amplitudes in N=4 Super-Yang-Mills
• Three-Loop Superfiniteness of N=8 Supergravity
• Supersymmetry Constraints on Type IIB Supergravity
• Pure Spinor Formalism as an N=2 Topological String
• Duality and higher derivative terms in M theory
• Ten-Dimensional Supergravity Constraints from the Pure Spinor Formalism for the Superstring
• Multiloop Amplitudes and Vanishing Theorems using the Pure Spinor Formalism for the Superstring
• E7(7) constraints on counterterms in N=8 supergravity
• The Complete Four-Loop Four-Point Amplitude in N=4 Super-Yang-Mills Theory
• Equivalence of Two-Loop Superstring Amplitudes in the Pure Spinor and RNS Formalisms
• Two-loop superstrings and S-duality
• Covariant Quantization of the Superparticle Using Pure Spinors
• Super-Poincare Covariant Two-Loop Superstring Amplitudes
• Non-renormalisation Conditions in Type II String Theory and Maximal Supergravity
• String theory dualities and supergravity divergences
• The No-Triangle Hypothesis for N=8 Supergravity
• New Higher-Derivative $R^4$ Theorems
• Multiloop Superstring Amplitudes from Non-Minimal Pure Spinor Formalism
• 5 loops in 24/5 dimensions
• Some Superstring Amplitude Computations with the Non-Minimal Pure Spinor Formalism
• Stringy KLT relations, global symmetries, and E_7(7) violation
• A simple approach to counterterms in N=8 supergravity
• Covariant One-Loop Amplitudes in D=11
• On duality symmetries of supergravity invariants
• GAMMA: A Mathematica package for performing gamma-matrix algebra and Fierz transformations in arbitrary dimensions
• Absence of Triangles in Maximal Supergravity Amplitudes
• Modular properties of two-loop maximal supergravity and connections with string theory
• Pure Spinor Vertex Operators in Siegel Gauge and Loop Amplitude Regularization
• D=11 supergravity with manifest supersymmetry
• Vertex Operators for Closed Superstrings
• Superstring Scattering Amplitudes with the Pure Spinor Formalism
• The Overall Coefficient of the Two-loop Superstring Amplitude Using Pure Spinors
• A note on the UV behaviour of maximally supersymmetric Yang-Mills theories
• Non-renormalization conditions for four-gluon scattering in supersymmetric string and field theory
• Pure Spinor Superspace Identities for Massless Four-point Kinematic Factors
• Higher-Dimensional Twistor Transforms using Pure Spinors
• Explicit Cancellation of Triangles in One-loop Gravity Amplitudes
• Worldline Green Functions for Arbitrary Feynman Diagrams
• Towards a manifestly supersymmetric action for 11-dimensional supergravity
• Finiteness and Unitarity of Lorentz-Covariant Green-Schwarz Superstring Amplitudes
• The critical ultraviolet behaviour of N=8 supergravity amplitudes
• One-loop Superstring Amplitude From Integrals on Pure Spinors Space
• Higher-loop amplitudes in the non-minimal pure spinor formalism
• The b Ghost of the Pure Spinor Formalism is Nilpotent
• A note on N=8 counterterms

Cited by in corpus (46)

• Simplifying Multiloop Integrands and Ultraviolet Divergences of Gauge Theory and Gravity Amplitudes
• Five-Point Amplitudes in N=4 Super-Yang-Mills Theory and N=8 Supergravity
• Enhanced Ultraviolet Cancellations in N = 5 Supergravity at Four Loop
• Ultraviolet Properties of N = 8 Supergravity at Five Loops
• Scattering amplitudes in N=2 Maxwell-Einstein and Yang-Mills/Einstein supergravity
• The Five-Loop Four-Point Integrand of N=8 Supergravity as a Generalized Double Copy
• The Structure of n-Point One-Loop Open Superstring Amplitudes
• The Ultraviolet Structure of Half-Maximal Supergravity with Matter Multiplets at Two and Three Loops
• The vanishing volume of D=4 superspace
• Nonlocal quantum gravity and M-theory
• Generic multiloop methods and application to N=4 super-Yang-Mills
• Ultraviolet Cancellations in Half-Maximal Supergravity as a Consequence of the Double-Copy Structure
• The two-loop five-point amplitude in $\mathcal{N}=8$ supergravity
• Non-linear gauge transformations in $D=10$ SYM theory and the BCJ duality
• N-Point Tree-Level Scattering Amplitude in the New Berkovits' String
• D = 5 maximally supersymmetric Yang-Mills theory diverges at six loops
• Color-kinematics duality and Sudakov form factor at five loops for N=4 supersymmetric Yang-Mills theory
• Pure spinor superfields -- an overview
• Amplitudes and Ultraviolet Behavior of N=8 Supergravity
• Tree-level amplitudes from the pure spinor superstring
• A solution to the non-linear equations of D=10 super Yang-Mills theory
• 10D Super-Yang-Mills Scattering Amplitudes From Its Pure Spinor Action
• Einstein gravity from the $\mathbb{N}=4$ spinning particle
• Pure spinor superfields and Born-Infeld theory
• One-loop monodromy relations on single cuts
• Ultraviolet behavior of 6D supersymmetric Yang-Mills theories and harmonic superspace
• Loop amplitudes in maximal supergravity with manifest supersymmetry
• The D^6 R^4 term from three loop maximal supergravity
• Double Copy from Tensor Products of Metric BV${}^{■}$-algebras
• Spinor frame formalism for amplitudes and constrained superamplitudes of 10D SYM and 11D supergravity
• Tree-Level Color-Kinematics Duality from Pure Spinor Actions
• One-loop SYM-supergravity relation for five-point amplitudes
• Gravity loop integrands from the ultraviolet
• Simplified D=11 Pure Spinor b Ghost
• The geometry of pure spinor space
• An off-shell superspace reformulation of D=4, N=4 super-Yang-Mills theory
• Notes on the $D=11$ pure spinor superparticle
• Ultraviolet divergences in maximal supergravity from a pure spinor point of view
• An Update on Perturbative N=8 Supergravity
• Scattering equations, supergravity integrands, and pure spinors
• Pure spinor indications of ultraviolet finiteness in D=4 maximal supergravity
• Two-loop superstring five-point amplitudes I: Construction via chiral splitting and pure spinors
• Constraining non--BPS interactions from counterterms in three loop maximal supergravity
• Higher-dimensional invariants in $6D$ super Yang-Mills theory
• Pure spinors and $D=11$ supergravity
• Off- and on-shell harmonic superspaces for 6D SYM theories