Review on High energy String Scattering Amplitudes and Symmetries of String Theory

Abstract

We review high energy symmetries of string theory at both the fixed angle or Gross regime (GR) and the fixed momentum transfer or Regge regime (RR). We calculated in details high energy string scattering amplitudes at arbitrary mass levels for both regimes. We discovered infinite linear relations among fixed angle string amplitudes conjectured by Gross in 1988 from decoupling of high energy zero-norm states (ZNS), and infinite recurrence relations among Regge string amplitudes from Kummer function U and Appell function F_1. However, the linear relations we obtained in the GR corrected [27-32] the saddle point calculations of Gross, Gross and Mende and Gross and Manes [1-5]. Our results were consistent with the decoupling of high energy ZNS or unitarity of the theory while those of them were not. In addition, for the case of high energy closed string scatterings, our results [36] differ from theirs by an oscillating prefactor which was crucial to recover the KLT relation valid for all energies. In the GR/RR regime, all high energy string amplitudes can be solved by these linear/recurrence relations so that all GR/RR string amplitudes can be expressed in terms of one single GR/RR string amplitude. In addition, we found an interesting link between string amplitudes of the two regimes, and discovered that at each mass level the ratios among fixed angle amplitudes can be extracted from Regge string scattering amplitudes. This result enables us to argue that the known SL(5,C) dynamical symmetry of the Appell function F_1 is crucial to probe high energy spacetime symmetry of string theory.

315 pages. 4 figures. invited review article prepared for Symmetry. To be published in Symmetry (2015). V2:316 pages,4 figures. Eqs,Refs and paragraphs added. typos corrected. V3:341 pages,much more details for "Introduction and Overview", Refs and Appendices added. V4 : 341 pages, one paragraph added in abstract,Ref 9 added

References in corpus (15)

• The Pomeron and Gauge/String Duality
• Minimal Basis for Gauge Theory Amplitudes
• Gravitational effects in ultrahigh-energy string scattering
• Linear Relations and their Breakdown in High Energy Massive String Scatterings in Compact Spaces
• Patterns of High energy Massive String Scatterings in the Regge regime
• Notes on High Energy Limit of Bosonic Closed String Scattering Amplitudes
• Scatterings of Massive String States from D-brane and Their Linear Relations at High Energies
• The Appell Function $F_1$ and Regge String Scattering Amplitudes
• To see Symmetry in a Forest of Trees
• Kummer function and High energy String Scatterings
• High-energy Massive String Scatterings from Orientifold Planes
• The Exact SL(K+3,C) Symmetry of String Scattering Amplitudes
• Recurrence Relations of Higher Spin BPST Vertex Operators for Open String
• Power-law Behavior of Strings Scattered from Domain-wall at High Energies and Breakdown of their Linear Relations
• Stirling number Identities and High energy String Scatterings

Cited by in corpus (15)

• More on Quantum Chiral Higher Spin Gravity
• Supersymmetric Reducible Higher-Spin Multiplets in Various Dimensions
• The Lauricella Functions and Exact String Scattering Amplitudes
• Deformation of the Cubic Open String Field Theory
• Covariant open bosonic string field theory on multiple D-branes in the proper-time gauge
• String Scattering Amplitudes and Deformed Cubic String Field Theory
• The SL(K+3,C) Symmetry of the Bosonic String Scattering Amplitudes
• Solving Lauricella String Scattering Amplitudes through Recurrence Relations
• Spin polarization independence of hard polarized fermion string scattering amplitudes
• The exact SL(K+3,C) symmetry of string theory
• Scattering and Strebel graphs
• Asymptotic safety and quantum gravity amplitudes
• New bosonic hard string scattering amplitudes and extended Gross conjecture in superstring theory
• Residues of bosonic string scattering amplitudes and the Lauricella functions
• Comment on "High Energy Symmetry of String Theory"