A note on on-shell recursion relation of string amplitudes

Chang, Yung-Yeh; Feng, Bo; Fu, Chih-Hao; Lee, Jen-Chi; Wang, Yihong; Yang, Yi

doi:10.1007/jhep02(2013)028

Cited by 13 publications

(14 citation statements)

References 29 publications

(75 reference statements)

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“…[13], but they are unwieldy even before taking sums over products of them. Some headway on this problem was made in [14] by summing over spurious states, but to our knowledge no complete solution exists.…”

Section: Contentsmentioning

confidence: 99%

String theory in target space

Boels

Hansen

2014

J. High Energ. Phys.

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It is argued that the complete S-matrix of string theory at tree level in a flat background can be obtained from a small set of target space properties, without recourse to the worldsheet description. The main non-standard inputs are (generalised) BrittoCachazo-Feng-Witten shifts, as well as the monodromy relations for open string theory and the Kawai-Lewellen-Tye relations for closed string theory. The roots of the scattering amplitudes and especially their appearance in the residues at the kinematic poles are central to the story. These residues determine the amplitudes through on-shell recursion relations. Several checks of the formalism are presented, including a computation of the Koba-Nielsen amplitude in the bosonic string. Furthermore the question of target space unitarity is (re-)investigated. For the Veneziano amplitude this question is reduced by Poincaré invariance, unitarity and locality to that of positivity of a particular numerical sum. Interestingly, this analysis produces the main conditions of the no-ghost theorem on dimension and intercept from the first three poles of this amplitude.

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Section: Contentsmentioning

confidence: 99%

String theory in target space

Boels

Hansen

2014

J. High Energ. Phys.

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“…Recently, five-point tachyon amplitude was considered in the context of BCFW application of string theory in [34]. It will be interesting to consider both RR and GR of higher spin five-point scattering amplitudes.…”

Section: Recurrence Relations and Rr Stringy Ward Identitiesmentioning

confidence: 99%

Recurrence relations of Kummer functions and Regge string scattering amplitudes

Lee

Mitsuka

2013

J. High Energ. Phys.

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We discover an infinite number of recurrence relations among Regge string scattering amplitudes [10, 23] of different string states at arbitrary mass levels in the open bosonic string theory. As a result, all Regge string scattering amplitudes can be algebraically solved up to multiplicative factors. Instead of decoupling zero-norm states in the fixed angle regime, the calculation is based on recurrence relations and addition theorem of Kummer functions of the second kind. These recurrence relations among Regge string scattering amplitudes are dual to linear relations or symmetries among high-energy fixed angle string scattering amplitudes discovered previously.

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“…For the 5-point KN amplitude, a simple generalization of Eq. (3.3) is to use the string theory extension [44] of field theory BCFW on-shell recursion relations [47,48] to calculate the infinite number of residues. Moreover, we will show that all residues can be expressed in terms of the Lauricella functions.…”

Section: B the Five Point Kn Amplitudementioning

confidence: 99%

“…In this paper, we will apply the string theory extension [44], [45,46] of field theory BCFW on-shell recursion relations [47,48] to calculate explicitly residues of all n-point Koba-Nielsen (KN) amplitudes. In addition, we will show that the residues of all SSA including the KN amplitudes can be expressed in terms of the Lauricella functions.…”

Section: Introductionmentioning

confidence: 99%

Residues of bosonic string scattering amplitudes and the Lauricella functions

Lai¹,

Lee

Yang

2021

Preprint

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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.

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A note on on-shell recursion relation of string amplitudes

Cited by 13 publications

References 29 publications

String theory in target space

String theory in target space

Recurrence relations of Kummer functions and Regge string scattering amplitudes

Residues of bosonic string scattering amplitudes and the Lauricella functions

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