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

Abstract

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.

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

“…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].…”

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

“…Indeed, it was found [8] that the saddle point calculation of open HSS amplitudes was applicable only for the t−u channel, but not reliable for the s−t channel, neither for the closed HSS amplitude calculation. In addition, it was also pointed out [8,23] that the prefactor sin(πu/2) sin(πs/2) in the string BCJ relations, which was missing in the literature [9][10][11][12][13]24] for the HSS amplitude calculations, had important physical interpretations. The poles give infinite number of resonances in the string spectrum and zeros give the coherence of string scatterings.…”

“…In section II, we will first review the extended linear relations in the HSS limit discussed in [8]. We will also work out the corresponding extended recurrence relations [25,26] of the Regge string scattering (RSS) amplitudes [27].…”

“…The first "string BCJ relation" discovered was the four point string BCJ relation in the HSS limit [8] …”

“…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.…”