New Higher-Derivative $R^4$ Theorems

Abstract

The non-minimal pure spinor formalism for the superstring is used to prove two new multiloop theorems which are related to recent higher-derivative $R^4$ conjectures of Green, Russo and Vanhove. The first theorem states that when $0<n<12$, ${\partial }^n{R}^4$ terms in the Type II effective action do not receive perturbative contributions above $n/2$ loops. The second theorem states that when $n\le 8$, perturbative contributions to ${\partial }^n{R}^4$ terms in the IIA and IIB effective actions coincide.

10 pages harvmac

References in corpus (15)

• Super-Poincare Covariant Quantization of the Superstring
• On the Relationship between Yang-Mills Theory and Gravity and its Implication for Ultraviolet Divergences
• Effects of D-instantons
• One loop in eleven dimensions
• Pure Spinor Formalism as an N=2 Topological String
• D-instantons, Strings and M-theory
• Duality and higher derivative terms in M theory
• Two loops in eleven dimensions
• Is N = 8 Supergravity Ultraviolet Finite?
• 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
• Super-Poincare Covariant Two-Loop Superstring Amplitudes
• Non-renormalisation Conditions in Type II String Theory and Maximal Supergravity
• Multiloop Superstring Amplitudes from Non-Minimal Pure Spinor Formalism

Cited by in corpus (74)

• What is the Simplest Quantum Field Theory?
• A Duality For The S Matrix
• The Ultraviolet Behavior of N=8 Supergravity at Four Loops
• Manifest Ultraviolet Behavior for the Three-Loop Four-Point Amplitude of N=8 Supergravity
• The S-Matrix in Twistor Space
• E7(7) constraints on counterterms in N=8 supergravity
• Ultraviolet Properties of N = 8 Supergravity at Five Loops
• The Complete Four-Loop Four-Point Amplitude in N=4 Super-Yang-Mills Theory
• Ultraviolet properties of Maximal Supergravity
• The closed-string 3-loop amplitude and S-duality
• Unexpected Cancellations in Gravity Theories
• Automorphic properties of low energy string amplitudes in various dimensions
• String theory dualities and supergravity divergences
• Supertwistor space for 6D maximal super Yang-Mills
• 5 loops in 24/5 dimensions
• Genus-One String Amplitudes from Conformal Field Theory
• Stringy KLT relations, global symmetries, and E_7(7) violation
• A simple approach to counterterms in N=8 supergravity
• The ultra-violet question in maximally supersymmetric field theories
• How Far Are We from the Quantum Theory of Gravity?
• Multiparticle SYM equations of motion and pure spinor BRST blocks
• Multi-loop amplitudes in maximally supersymmetric pure spinor field theory
• New Modular Invariants in $\mathcal{N}=4$ Super-Yang-Mills Theory
• R^4 counterterm and E7(7) symmetry in maximal supergravity
• The D^4 R^4 term in type IIB string theory on T^2 and U-duality
• Simplifying the Tree-level Superstring Massless Five-point Amplitude
• The Overall Coefficient of the Two-loop Superstring Amplitude Using Pure Spinors
• M-Theory Reconstruction from (2,0) CFT and the Chiral Algebra Conjecture
• On the Structure of Supersymmetric Sums in Multi-Loop Unitarity Cuts
• Non-renormalization conditions for four-gluon scattering in supersymmetric string and field theory
• Tree-level amplitudes from the pure spinor superstring
• Explicit Cancellation of Triangles in One-loop Gravity Amplitudes
• Simplicity in the Structure of QED and Gravity Amplitudes
• Poisson equation for the Mercedes diagram in string theory at genus one
• Unraveling L_{n,k}: Grassmannian Kinematics
• The One-loop Open Superstring Massless Five-point Amplitude with the Non-Minimal Pure Spinor Formalism
• Superstring loop amplitudes from the field theory limit
• Covariant actions for models with non-linear twisted self-duality
• N=8 Supergravity on the Light Cone
• N=8 Supergravity 4-point Amplitudes
• GGI Lectures on the Pure Spinor Formalism of the Superstring
• SUSY Ward identities, Superamplitudes, and Counterterms
• Poisson equation for the three loop ladder diagram in string theory at genus one
• Cohomology foundations of one-loop amplitudes in pure spinor superspace
• The critical ultraviolet behaviour of N=8 supergravity amplitudes
• D=11 massless superparticle covariant quantization, pure spinor BRST charge and hidden symmetries
• Spinor moving frame, M0-brane covariant BRST quantization and intrinsic complexity of the pure spinor approach
• The D^{10} R^4 term in type IIB string theory
• Higher-loop amplitudes in the non-minimal pure spinor formalism
• On UV Finiteness of the Four Loop N=8 Supergravity
• On Cancellations of Ultraviolet Divergences in Supergravity Amplitudes
• The D^6 R^4 term in type IIB string theory on T^2 and U-duality
• Interpolating the Coulomb Phase of Little String Theory
• Perturbation Theory From Automorphic Forms
• The D^6 R^4 term from three loop maximal supergravity
• Constraints on Automorphic Forms of Higher Derivative Terms from Compactification
• Constraining the D3-brane effective action
• A simplifying feature of the heterotic one loop four graviton amplitude
• One-loop N=8 supergravity coefficients from N=4 super Yang-Mills
• 1/8-BPS Couplings and Exceptional Automorphic Functions
• Perturbative type II amplitudes for BPS interactions
• Decoupling of unphysical states in the minimal pure spinor formalism I
• Higher derivative type II string effective actions, automorphic forms and E11
• An Alternative Canonical Approach to the Ghost Problem in a Complexified Extension of the Pais-Uhlenbeck Oscillator
• A Note on Single Soft Scalar Emission of $\mathcal{N}=8$ SUGRA and $E_{7(7)}$ Symmetry
• Decoupling of unphysical states in the minimal pure spinor formalism II
• Constraining gravitational interactions in the M theory effective action
• Black Hole Partition Function using Hybrid Formalism of Superstrings
• Twistors, strings and supersymmetric gauge theories
• Non-analytic terms of string amplitudes from partial waves
• Parameters, limits and higher derivative type II string corrections
• Non--analytic terms from nested divergences in maximal supergravity
• Infrared Finite Observables in N=8 Supergravity
• Some finite terms from ladder diagrams in three and four loop maximal supergravity