Recent developments of the Lauricella string scattering amplitudes and their exact SL(K+3,C) Symmetry

Abstract

In this review we propose a new perspective to demonstrate Gross conjecture on high energy symmetry of string theory. We review the construction of the exact string scattering amplitudes (SSA) of three tachyons and one arbitrary string state, or the Lauricella SSA (LSSA), in the 26D open bosonic string theory. These LSSA form an infinite dimensional representation of the SL(K+3,C) group. Moreover, we show that the SL(K+3,C) group can be used to solve all the LSSA and express them in terms of one amplitude. As an application in the hard scattering limit, the LSSA can be used to directly prove Gross conjecture which was previously corrected and proved by the method of decoupling of zero norm states (ZNS). Finally, the exact LSSA can be used to rederive the recurrence relations of SSA in the Regge scattering limit with associated SL(5,C) symmetry and the extended recurrence relations (including the mass and spin dependent string BCJ relations) in the nonrelativistic scattering limit with associated SL(4,C) symmetry discovered recently.

arXiv comment54 pages, 1 figure, minor modification, references added. arXiv admin note: text overlap with arXiv:1806.05033

References in corpus (34)

• New Relations for Gauge-Theory Amplitudes
• Nonlinear Equations for Symmetric Massless Higher Spin Fields in $(A)d{S}_d$
• Minimal Basis for Gauge Theory Amplitudes
• On higher spins and the tensionless limit of String Theory
• Tensionless Strings and the Weak Gravity Conjecture
• Higher Spins & Strings
• Tensionless Strings from Worldsheet Symmetries
• More on Quantum Chiral Higher Spin Gravity
• Direct Production of Lightest Regge Resonances
• Stringy Symmetries and Their High-energy Limits
• Zero-norm states and High-energy Symmetries of String Theory
• Solving all 4-point correlation functions for bosonic open string theory in the high energy limit
• Rindler on the Worldsheet
• Ward Identities and High-energy Scattering Amplitudes in String Theory
• T-duality Constraints on Higher Derivatives Revisited
• High-energy zero-norm states and symmetries of string theory
• Discrete Gauge States and$w_{\infty }$ Charges in c=1 2d Gravity
• DDF operators, open string coherent states and their scattering amplitudes
• The covariant perturbative string spectrum
• High Energy Scattering Amplitudes of Superstring Theory
• On stable higher spin states in Heterotic String Theories
• Patterns of High energy Massive String Scatterings in the Regge regime
• Notes on High Energy Limit of Bosonic Closed String Scattering Amplitudes
• Galilean Yang-Mills Theory
• Supersymmetric Reducible Higher-Spin Multiplets in Various Dimensions
• G2HDM : Gauged Two Higgs Doublet Model
• String coherent vertex operators of Neveu-Schwarz and Ramond states
• The Lauricella Functions and Exact String Scattering Amplitudes
• Recurrence relations of Kummer functions and Regge string scattering amplitudes
• The Appell Function $F_1$ and Regge String Scattering Amplitudes
• Solving Lauricella String Scattering Amplitudes through Recurrence Relations
• Spin polarization independence of hard polarized fermion string scattering amplitudes
• Plahte Diagrams for String Scattering Amplitudes
• The String BCJ Relations Revisited and Extended Recurrence relations of Nonrelativistic String Scattering Amplitudes

Cited by in corpus (4)

• The exact SL(K+3,C) symmetry of string theory
• New bosonic hard string scattering amplitudes and extended Gross conjecture in superstring theory
• The $SL(K+3,\mathbb{C})$ symmetry of string scatterings from D-branes
• The stringy scaling loop expansion and stringy scaling violation