Solving all 4-point correlation functions for bosonic open string theory in the high-energy limit

Chan, Chuan Tsung; Ho, Pei-Ming; Lee, Jen Chi; Teraguchi, Shunsuke; Yang, Yi

doi:10.1016/j.nuclphysb.2005.07.018

Cited by 59 publications

(210 citation statements)

References 37 publications

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“…This is physically consistent as one expects a m R , 1 2 nR dependent Regge-pole and zero structures in the high energy string scattering amplitudes. In conclusion, in the GR, Presumably, the infinite linear relations obtained above can be reproduced by using the method of high energy ZNS, or high energy Ward identities, adopted in the previous works [4,5,6,7,8,9,10,11]. The existence of Soliton ZNS at arbitrary mass levels was constructed in [22].…”

Section: B the Infinite Linear Relations In The Grmentioning

confidence: 81%

Linear relations and their breakdown in high energy massive string scatterings in compact spaces

Lee

Yang

2007

Nuclear Physics B

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We calculate high energy massive scattering amplitudes of closed bosonic string compactified on the torus. For each fixed mass level with given quantized and winding momenta m R , 1 2 nR , we obtain infinite linear relations among high energy scattering amplitudes of different string states.For some kinematic regimes, we discover that linear relations with N R = N L break down and, simultaneously, the amplitudes enhance to power-law behavior instead of the usual expoential falloff behavior at high energies. It is the space-time T-duality symmetry that plays a role here.This result is consistent with the coexistence of the linear relations and the softer exponential fall-off behavior of high energy string scattering amplitudes as we pointed out prevously. It is also reminiscent of our previous work on the power-law behavior of high energy string/domain-wall scatterings. *

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Section: B the Infinite Linear Relations In The Grmentioning

confidence: 81%

Linear relations and their breakdown in high energy massive string scatterings in compact spaces

Lee

Yang

2007

Nuclear Physics B

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“…The next key step was that the result of eq. (2.6) can be generalized to the case of three tachyons and one arbitrary string states [18,19], and then to the case of four arbitrary string states. This generalization was based on the important result that, at each fixed mass level N, the high energy fixed angle string scattering amplitudes for states differ from leading Regge trajectory higher spin state in the second vertex are all proportional to each other [18,19] …”

Section: Jhep05(2016)186mentioning

confidence: 99%

“…This was the discovery of the four point string BCJ relations in the high energy fixed angle or hard string scattering (HSS) limit in 2006 [8]. Moreover, one can combine these string BCJ relations with the infinite linear relations among HSS amplitudes conjectured by Gross [9][10][11][12][13] and discovered in [14][15][16][17][18][19][20] to form the extended linear relations in the HSS limit. For a recent review, see [21].…”

Section: Introductionmentioning

confidence: 99%

The string BCJ relations revisited and extended recurrence relations of nonrelativistic string scattering amplitudes

Lai

Lee²,

Yang³

2016

J. High Energ. Phys.

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We review and extend high energy four point string BCJ relations in both the fixed angle and Regge regimes. We then give an explicit proof of four point string BCJ relations for all energy. This calculation provides an alternative proof of the one based on monodromy of integration in string amplitude calculation. In addition, we calculate both s − t and t − u channel nonrelativistic low energy string scattering amplitudes of three tachyons and one higher spin string state at arbitrary mass levels. We discover that the mass and spin dependent nonrelativistic string BCJ relations can be expressed in terms of Gauss hypergeometry functions. As an application, for each fixed mass level N, we derive extended recurrence relations among nonrelativistic low energy string scattering amplitudes of string states with different spins and different channels.

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“…Another evidence for this point is the following. When one uses the saddle point method to calculate the high-energy open string scattering amplitudes in the (s, t) channel, the saddle-point we identified was [6,7,8] …”

Section: Saddle Point Calculationmentioning

confidence: 99%

“…Recently high-energy, fixed-angle behavior of string scattering amplitudes [1,2,3] was intensively reinvestigated [4,5,6,7,8,9,10]. The motivation was to uncover the long-sought hidden stringy space-time symmetry.…”

Section: Introductionmentioning

confidence: 99%

Notes on high-energy limit of bosonic closed string scattering amplitudes

2006

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We study bosonic closed string scattering amplitudes in the high-energy limit. We find that the methods of decoupling of high-energy zero-norm states and the high-energy Virasoro constraints, which were adopted in the previous works to calculate the ratios among high-energy open string scattering amplitudes of different string states, persist for the case of closed string. However, we clarify the previous saddle-point calculation for high-energy open string scattering amplitudes and claim that only (t, u) channel of the amplitudes is suitable for saddle-point calculation. We then discuss three evidences to show that saddle-point calculation for high-energy closed string scattering amplitudes is not reliable. By using the relation of tree-level closed and open string scattering amplitudes of Kawai, Lewellen and Tye (KLT), we calculate the high-energy closed string scattering amplitudes for arbitrary mass levels. For the case of high-energy closed string four-tachyon amplitude, our result differs from the previous one of Gross and Mende, which is NOT consistent with KLT formula, by an oscillating factor.

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Solving all 4-point correlation functions for bosonic open string theory in the high-energy limit

Cited by 59 publications

References 37 publications

Linear relations and their breakdown in high energy massive string scatterings in compact spaces

Linear relations and their breakdown in high energy massive string scatterings in compact spaces

The string BCJ relations revisited and extended recurrence relations of nonrelativistic string scattering amplitudes

Notes on high-energy limit of bosonic closed string scattering amplitudes

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