Linear relations among four-point functions in the high energy limit of string theory

Abstract

The decoupling of zero-norm states leads to linear relations among 4-point functions in the high energy limit of string theory. Recently it was shown that the linear relations uniquely determine ratios among 4-point functions at the leading order. The purpose of this paper is to extend the validity of the same approach to the next-to-leading order and higher orders.

High-energy symmetry of bosonic open string theory in the light-like linear dilaton background

“…provide the polarization tensor (ǫ µν , ǫ µ ) satisfies the physical state condition Eqs. (19) and (21).…”

“…We emphasize that in the calculations of all three-point functions, the full vertex operators, Eqs. (14), (15), (16) are used for each physical state. Thus, using Eqs.…”

“…(3) Our main concern in the present study is to explore the symmetry pattern for highenergy stringy scattering amplitudes of different total level. One of the early attempt for studying the subleading high-energy stringy scattering amplitudes can be found in [15]. Here we wish to push the idea further, and indeed we can identify a set of replacement rules (ignoring the phase factors) for relating different high-energy stringy scattering amplitudes.…”

“…For a given conformal invariant background, we need to solve for the spectrum of stringy excitations and calculate the scattering amplitudes separately. One can gather many useful information and interesting patterns from different backgrounds and various kinematic limits [13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]. However, if we wish to look for a symmetry principle underlying string theory, we should be able to relate these symmetry patterns and extract a universal property from these calculations.…”

“…In a later reinvestigation of this problem [8,9,10,11,12,13,14,15], the authors have clarified some of the important issues related to the high-energy stringy symmetry (HESS):…”