High-Energy Zero-Norm States and Symmetries of String Theory

Abstract

High-energy limit of zero-norm states in the old covariant first quantized spectrum of the 26D open bosonic string, together with the assumption of a smooth behavior of string theory in this limit, are used to derive infinitely many linear relations among the leading high-energy, fixed-angle behavior of four-point functions of different string states. As a result, ratios among all high-energy scattering amplitudes of four arbitrary string states can be calculated algebraically and the leading order amplitudes can be expressed in terms of that of four tachyons as conjectured by Gross in 1988. A dual calculation can also be performed and equivalent results are obtained by taking the high-energy limit of Virasoro constraints. Finally, we compute all high-energy scattering amplitudes of three tachyons and one massive state at the leading order by saddle-point approximation to verify our results.

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].…”

Massive superstring scatterings in the Regge regime

“…For simplicity, we choose k 1 , k 3 and k 4 to be tachyons. It turns out that all scattering amplitudes at each fixed mass level are proportional to each other, and the final result for the ratios of high energy, fixed angle string scattering amplitude are [7,8] …”

“…These two regimes represent two different high energy perturbation expansions of the scattering amplitudes, and contain complementary information of the theory. The high energy string scattering amplitudes in the GR [1][2][3] were recently intensively reinvestigated for massive string states at arbitrary mass levels [4][5][6][7][8][9][10][11][12][13]. See also the developments in [14][15][16].…”

Recurrence relations of higher spin BPST vertex operators for open strings

“…One of the motivations was to understand their intimate link with the scattering amplitudes in the fixed-angle or Gross regime (GR) [11][12][13][14][15]. In the GR, a saddle-point method was used to calculate string-tree amplitudes [16][17][18][19], and the ratios of scattering amplitudes among different string states at each fixed mass level can be extracted and were found to be independent of the scattering energy and scattering angle. Alternatively, these ratios can be rederived algebraically by solving linear relations or GR stringy Ward identities from decoupling of zero-norm states (ZNS) [20][21][22].…”