Non-abelian $Z$-theory: Berends-Giele recursion for the ${\alpha }^{\prime }$-expansion of disk integrals

Abstract

We present a recursive method to calculate the ${\alpha }^{\prime }$-expansion of disk integrals arising in tree-level scattering of open strings which resembles the approach of Berends and Giele to gluon amplitudes. Following an earlier interpretation of disk integrals as doubly partial amplitudes of an effective theory of scalars dubbed as $Z$-theory, we pinpoint the equation of motion of $Z$-theory from the Berends-Giele recursion for its tree amplitudes. A computer implementation of this method including explicit results for the recursion up to order ${\alpha }^{\prime 7}$ is made available on the website http://repo.or.cz/BGap.git

arXiv comment58 pages, harvmac TeX, v2: cosmetic changes, published version

References in corpus (68)

• Direct Proof Of Tree-Level Recursion Relation In Yang-Mills Theory
• New Relations for Gauge-Theory Amplitudes
• Harmonic Polylogarithms
• Perturbative Quantum Gravity as a Double Copy of Gauge Theory
• New features of FORM
• Super-Poincare Covariant Quantization of the Superstring
• FORM version 4.0
• Scattering of Massless Particles: Scalars, Gluons and Gravitons
• Multi-Leg One-Loop Gravity Amplitudes from Gauge Theory
• Minimal Basis for Gauge Theory Amplitudes
• Algorithms for the symbolic integration of hyperlogarithms with applications to Feynman integrals
• Scattering Equations and Matrices: From Einstein To Yang-Mills, DBI and NLSM
• The Multiple Zeta Value Data Mine
• Multiple polylogarithms and mixed Tate motives
• From polygons and symbols to polylogarithmic functions
• The Momentum Kernel of Gauge and Gravity Theories
• Explicit BCJ Numerators from Pure Spinors
• Polylogarithms, Multiple Zeta Values and Superstring Amplitudes
• Open & Closed vs. Pure Open String Disk Amplitudes
• Elliptic multiple zeta values and one-loop superstring amplitudes
• Soft triple-real radiation for Higgs production at N3LO
• Motivic Multiple Zeta Values and Superstring Amplitudes
• The massless higher-loop two-point function
• Analytic and Algorithmic Aspects of Generalized Harmonic Sums and Polylogarithms
• Closed String Amplitudes as Single-Valued Open String Amplitudes
• On the modular structure of the genus-one Type II superstring low energy expansion
• Gravity and Yang-Mills Amplitude Relations
• Closed Superstring Amplitudes, Single-Valued Multiple Zeta Values and Deligne Associator
• Feynman integrals and hyperlogarithms
• The open superstring 5-point amplitude revisited
• Multi-Gluon Scattering in Open Superstring Theory
• On amplitudes in self-dual sector of Yang-Mills theory
• Berends-Giele recursion for double-color-ordered amplitudes
• Tree-level Amplitudes in the Nonlinear Sigma Model
• Exact solutions for the biadjoint scalar field
• The structure of maximally supersymmetric Yang-Mills theory: constraining higher-order corrections
• All order alpha'-expansion of superstring trees from the Drinfeld associator
• Multiparticle SYM equations of motion and pure spinor BRST blocks
• A recursive method for SYM n-point tree amplitudes
• On tree-level higher order gravitational couplings in superstring theory
• Non-linear gauge transformations in $D=10$ SYM theory and the BCJ duality
• Six Gluon Open Superstring Disk Amplitude, Multiple Hypergeometric Series and Euler-Zagier Sums
• Higher-loop amplitude monodromy relations in string and gauge theory
• D=10 Super-Yang-Mills at O(alpha'^2)
• Universality in string interactions
• Proving relations between modular graph functions
• 5-field terms in the open superstring effective action
• On-shell Recursion in String Theory
• Supersymmetric Yang-Mills theory at order alpha'^3
• RNS derivation of N-point disk amplitudes from the revisited S-matrix approach
• MHV, CSW and BCFW: field theory structures in string theory amplitudes
• On the field theory expansion of superstring five point amplitudes
• Pure Spinor Superspace Identities for Massless Four-point Kinematic Factors
• Proof of a modular relation between 1-, 2- and 3-loop Feynman diagrams on a torus
• Poisson equation for the Mercedes diagram in string theory at genus one
• BCFW Recursion Relations and String Theory
• Superstring amplitudes and the associator
• MPL - a program for computations with iterated integrals on moduli spaces of curves of genus zero
• Simplifying the one loop five graviton amplitude in type IIB string theory
• Poisson equation for the three loop ladder diagram in string theory at genus one
• Superstring Amplitudes as a Mellin Transform of Supergravity
• Symmetry Breaking at enhanced Symmetry Points
• Complete N-Point Superstring Disk Amplitude I. Pure Spinor Computation
• Differential Equations, Associators, and Recurrences for Amplitudes
• The cohomology of superspace, pure spinors and invariant integrals
• Spinorial cohomology of abelian d=10 super-Yang-Mills at alpha'^3
• D=10 supersymmetric Yang-Mills theory at alpha'^4
• Hierarchy of Modular Graph Identities

Cited by in corpus (70)

• Abelian Z-theory: NLSM amplitudes and alpha'-corrections from the open string
• Ultraviolet Properties of N = 8 Supergravity at Five Loops
• Combinatorics and Topology of Kawai-Lewellen-Tye Relations
• Aspects of Scattering Amplitudes and Moduli Space Localization
• The Five-Loop Four-Point Integrand of N=8 Supergravity as a Generalized Double Copy
• Gravity Amplitudes as Generalized Double Copies
• New BCJ representations for one-loop amplitudes in gauge theories and gravity
• Semi-abelian Z-theory: NLSM+phi^3 from the open string
• Heterotic and bosonic string amplitudes via field theory
• A new gauge-invariant double copy for heavy-mass effective theory
• On the kinematic algebra for BCJ numerators beyond the MHV sector
• Perturbiner Methods for Effective Field Theories and the Double Copy
• Extended solutions for the biadjoint scalar field
• From elliptic multiple zeta values to modular graph functions: open and closed strings at one loop
• Off-Shell Color-Kinematics Duality for Chern-Simons
• Carving out the Space of Open-String S-matrix
• Simple encoding of higher derivative gauge and gravity counterterms
• Scattering Equations: From Projective Spaces to Tropical Grassmannians
• Inverse of the String Theory KLT Kernel
• Tree-level amplitudes from the pure spinor superstring
• Double-Copy Structure of One-Loop Open-String Amplitudes
• Closed strings as single-valued open strings: A genus-zero derivation
• Composing Effective Prediction at Five Points
• String amplitudes from field-theory amplitudes and vice versa
• All-order differential equations for one-loop closed-string integrals and modular graph forms
• Berends-Giele currents in Bern-Carrasco-Johansson gauge for $F^3$- and $F^4$-deformed Yang-Mills amplitudes
• Twisted elliptic multiple zeta values and non-planar one-loop open-string amplitudes
• One-loop open-string integrals from differential equations: all-order alpha'-expansions at n points
• Labelled tree graphs, Feynman diagrams and disk integrals
• Towards the n-point one-loop superstring amplitude III: One-loop correlators and their double-copy structure
• $L_{\infty }$-algebras and the perturbiner expansion
• Heterotic-string amplitudes at one loop: modular graph forms and relations to open strings
• Amplitudes, Hopf algebras and the colour-kinematics duality
• Tetrahedral modular graph functions
• New recursions for tree-level correlators in (Anti) de Sitter space
• String Correlators: Recursive Expansion, Integration-by-Parts and Scattering Equations
• Scalar-Scaffolded Gluons and the Combinatorial Origins of Yang-Mills Theory
• A Vertex Operator Algebra Construction of the Colour-Kinematics Dual numerator
• All-order alpha'-expansion of one-loop open-string integrals
• Biadjoint scalar tree amplitudes and intersecting dual associahedra
• Kinematic Hopf algebra for amplitudes and form factors
• A note on the Drinfeld associator for genus-zero superstring amplitudes in twisted de Rham theory
• Coaction and double-copy properties of configuration-space integrals at genus zero
• One-loop off-shell amplitudes from classical equations of motion
• A Lie bracket for the momentum kernel
• The $L_{\infty }$ structure of gauge theories with matter
• Amplitude recursions with an extra marked point
• Multiparticle solutions to Einstein's equations
• The Color-Dual Fates of $F^3$, $R^3$, and $\mathcal{N}=4$ Supergravity
• Stokes Polytopes and Intersection Theory
• Bosonic sectorized strings and the $(DF{)}^2$ theory
• A Type of Unifying Relation in (A)dS Spacetime
• A String Deformation of the Parke-Taylor Factor
• Two dialects for KZB equations: generating one-loop open-string integrals
• On Polytopes and Generalizations of the KLT Relations
• Celestial Berends-Giele current
• BCJ, worldsheet quantum algebra and KZ equations
• Next-to-MHV Yang-Mills kinematic algebra
• Open-string integrals with multiple unintegrated punctures at genus one
• Moduli Space of Paired Punctures, Cyclohedra and Particle Pairs on a Circle
• KK-like relations of ${\alpha }^{\prime }$ corrections to disk amplitudes
• One-loop $N$-point correlators in pure gravity
• The double copy effective action: a quantum (chromodynamics) approach to space-time
• Blowing up Stringy Canonical Forms: An Algorithm to Win a Simplified Hironaka's Polyhedra Game
• Superstring amplitudes meet surfaceology
• $D$-Dimensional Modular Assembly of Higher-Derivative Four-Point Contact Amplitudes Involving Fermions
• One-loop matrix elements of effective superstring interactions: ${\alpha }^{\prime }$-expanding loop integrands
• Quantum Off-Shell Recursion Relation
• Closed form expression for the 5-point Veneziano amplitude in terms of 4-point amplitudes
• Entire Four-Graviton EFT from the Duality Between Color and Kinematics