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

Abstract

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. *

Power-law behavior of high energy string scatterings in compact spaces

“…In the Gross regime (GR), for each fixed mass level with given quantized and winding momenta nR , we obtain infinite linear relations among high energy scattering amplitudes of different string states. Moreover we discover that, for some kinematic regime, the so called Mende regime (MR), infinite linear relations with N R = N L break down and, simultaneously, the amplitudes enhance to power-law behavior [19]. It is the space-time T-duality symmetry that plays a role here.…”

“…One way to justify this conjecture (that is: the coexistence of the infinite linear relations and the softer exponential fall-off behavior of high energy string scatterings) is to find more examples of high energy string scatterings, which show the unusual hard power-law behavior and, simultaneously, give the breakdown of the infinite linear relations. With this in mind, in this report [19] we calculate high energy, fixed angle massive scattering amplitudes of closed bosonic string compactified on the torus [20]. In the Gross regime (GR), for each fixed mass level with given quantized and winding momenta nR , we obtain infinite linear relations among high energy scattering amplitudes of different string states.…”

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

“…Following the suggestion of Mende [62], the authors In [2,3] calculated high energy massive scattering amplitudes of bosonic string with some coordinates compactified on the torus [2,3]. Infinite linear relations among high energy scattering amplitudes of different string states in the Hard scattering limit were obtained.…”

“…In [2,3], for string scatterings in the compact space, the authors discovered the existence of a power-law regime at fixed angle and simultaneously the linear relations (symmetry) break down in this regime.…”

Massive superstring scatterings in the Regge regime

“…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].…”