Massive superstring scatterings in the Regge regime

Yang

2014

Physics Letters B

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We show that each 26D open bosonic Regge string scattering amplitude (RSSA) can be expressed in terms of one single Appell function F 1 in the Regge limit. This result enables us to derive infinite number of recurrence relations among RSSA at arbitrary mass levels, which are conjectured to be related to the known SL(5, C ) dynamical symmetry of F 1 . In addition, we show that these recurrence relations in the Regge limit can be systematically solved so that all RSSA can be expressed in terms of one amplitude. All these results are dual to high energy symmetries of fixed angle string scattering amplitudes discovered previously [4][5][6][7][8].

Section: Introductionmentioning

confidence: 99%

The Appell function F1 and Regge string scattering amplitudes

Yang

2014

Physics Letters B

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“…It was shown [1,7,8] that for the 26-dimensional open bosonic string states of the leading order in energy in the Regge limit at mass level, M 2 2 ¼ 2ðN À 1Þ, N ¼ P n;m;l>0 np n þ mq m þ lr l are of the form (we choose the second state of the four-point function to be the higher-spin string state)…”

Section: A a Spin-2 Statementioning

confidence: 99%

“…The four-point amplitude of the above state with three tachyons was calculated to be (from now on, we set M 2 ¼ M) [1,7,8] A ðp n ;q m Þ ¼…”

Section: B Higher-spin Statesmentioning

confidence: 99%

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Recurrence relations of higher spin BPST vertex operators for open strings

Tan

et al. 2013

Phys. Rev. D

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We calculate higher-spin Brower-Polchinski-Strassler-Tan (BPST) vertex operators for an open bosonic string and express these operators in terms of a Kummer function of the second kind. We derive an infinite number of recurrence relations among BPST vertex operators of different string states. These recurrence relations among BPST vertex operators lead to the recurrence relations among Regge string scattering amplitudes discovered recently.Note that the convention for s and t adopted here is different from the original BPST paper in Ref. [2].We first review the calculation of tachyon BPST vertex operator [2]. The s À t channel of an open-string fourtachyon amplitude can be written as *

“…These recurrence relations can be used to solve all RSS amplitudes and express them in terms of one single amplitude. Moreover, an interesting link between the HSS and the RSS amplitudes was discovered, and the ratios among fixed angle amplitudes can be extracted from RSS amplitudes [21,22].…”

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confidence: 99%

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

Yang

2019

Symmetry

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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.