To see symmetry in a forest of trees

2016

J. High Energ. Phys.

We discover that the 26D open bosonic string scattering amplitudes (SSA) of three tachyons and one arbitrary string state can be expressed in terms of the D-type Lauricella functions with associated SL(K + 3, C) symmetry. As a result, SSA and symmetries or relations among SSA of different string states at various limits calculated previously can be rederived. These include the linear relations first conjectured by Gross [1-5] and later corrected and proved in [6][7][8][9][10][11][12] in the hard scattering limit, the recurrence relations in the Regge scattering limit with associated SL(5, C) symmetry [24][25][26] and the extended recurrence relations in the nonrelativistic scattering limit with associated SL(4, C) symmetry [29] discovered recently. Finally, as an application, we calculate a new recurrence relation of SSA which is valid for all energies.

“…point method [1][2][3][4][5] and Moore's bracket algebra approach [20][21][22] of stringy symmetries. See a recent review [23] for some connections of these three approaches.…”

Section: Jhep11(2016)062mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The Lauricella functions and exact string scattering amplitudes

Lai

2016

J. High Energ. Phys.

“…There existed other approaches of stringy symmetries which include other studies of string collisions in the high energy, fixed momentum transfer regime [63][64][65][66][67][68][69], the Hagedorn transition at high temperature [89][90][91], vertex operator algebra for compactified spacetime or on a lattice [92][93][94], group theoretical approach of string [48,95].…”

Section: Discussionmentioning

confidence: 99%

Overview of High Energy String Scattering Amplitudes and Symmetries of String Theory

2019

Symmetry

We overview symmetries of string scattering amplitudes in the high energy limits of both the fixed angle or Gross regime (GR) and the fixed momentum transfer or Regge regime (RR). We calculated high energy string scattering amplitudes (SSA) at arbitrary mass levels for both regimes.We discovered the infinite linear relations among fixed angle string amplitudes and the infinite recurrence relations among Regge string amplitudes. The linear relations we obtained in the GR corrected the saddle point calculations by Gross, Gross and Mende. In addition, for the high energy closed string scatterings, our results differ from theirs by an oscillating prefactor which was crucial to recover the KLT relation valid for all energies.We showed that all the high energy string amplitudes can be solved by the linear or recurrence relations so that all the string amplitudes can be expressed in terms of a single string amplitude.We further found that, at each mass level, the ratios among the fixed angle amplitudes can be extracted from the Regge string scattering amplitudes.Finally, we review the recent developments on the discovery of infinite number of recurrence relations valid for all energies among Lauricella SSA. The symmetries or relations among SSA at various limits obtained previously can be exactly reproduced. It leads us to argue that the known SL(K + 3, C) dynamical symmetry of the Lauricella function maybe crucial to probe spacetime symmetry of string theory.

“…In contrast to QFT, string theory as a quantum theory of an extended string consists of an infinite number of particles with arbitrary high spins and masses in the spectrum. It is thus reasonable to believe that there exists a huge symmetry group [2][3][4] which relates these infinite number of couplings and soften the SSA in the hard scattering limit.…”

Section: Introductionmentioning

confidence: 99%

Residues of bosonic string scattering amplitudes and the Lauricella functions

Lai¹,

2021

Preprint

We calculate explicitly residues of all n-point Koba-Nielsen (KN) amplitudes by using on-shell recursion relation of string scattering amplitudes (SSA). In addition, we show that the residues of all SSA including the KN amplitudes can be expressed in terms of the Lauricella functions. This result demonstrates the exact SL(K + 3, C) symmetry of the tree-level open bosonic string theory.Moreover, we derive an iteration relation among the residues of a given SSA. This iteration relation is related to the SL(K + 3, C) symmetry and can presumably be used to soften the well-known hard SSA.