Observations on open and closed string scattering amplitudes at high energies

Abstract

We study massless open and closed string scattering amplitudes in flat space at high energies. Similarly to the case of AdS space, we demonstrate that, under the T-duality map, the open string amplitudes are given by the exponential of minus minimal surface areas whose boundaries are cusped closed loops formed by lightlike momentum vectors. We show further that the closed string amplitudes are obtained by gluing two copies of minimal surfaces along their cusped lightlike boundaries. This can be thought of as a manifestation of the Kawai-Lewellen-Tye (KLT) relation at high energies. We also discuss the KLT relation in AdS/CFT and its possible connection to amplitudes in N = 8 supergravity as well as the correlator/amplitude duality.

Einstein-Yang-Mills scattering amplitudes from scattering equations

“…These equations have made an appearance at various times in the literature in a variety of different contexts [3][4][5][6][7][8][9][10][11]. The scattering equations generically have (n − 3)!…”

Collinear limits beyond the leading order from the scattering equations

“…These equations have appeared a number of times in the literature in various contexts [18][19][20][21][22][23][24]. They are known to possess (n − 3)!…”

A combinatoric shortcut to evaluate CHY-forms

“…1 On the other hand, we must also have r i 1 = 1 because r 2 + · · · + r n = M = ord(D). 2 Hence the tableau for a r 1 ,··· ,r i−1 ,0,r i+1 ,··· ,rn has only the i-th row empty and all the other rows filled. The aforementioned preferred coloring leads to (n − 1) red tiles in total and the local duality relation represented by this colored tableau involves a r 1 ,··· ,r i 1 ,0,r i+1 ,··· ,rn and other coefficients that all have r i = 1, i.e.…”

“…The coefficients associated with the other three tableaux are worked out in the same fashion and take the following forms, a r 1 ,r 2 ,r 3 ,r 4 ,r 5 +1 = −1 ℓ 5 R(a r 1 ,r 2 ,r 3 ,r 4 ,r 5 +1 ) With all the coefficients fixed for the case of (3.17), it is now straightforward to evaluate the P 1 and B [1,2],1 terms in (3.14), by acting with the differential operator D. Explicitly, the P 1 term becomes The integrand term containing B [1,2],1 is holomorphically equivalent to…”

“…Scattering equations are derived at tree level for the high-energy behavior of string theory in [1,2] and have drawn attention from theoretical physicists in diversified contexts [3,4]. Incorporating scattering equations, Cachazo, He and Yuan [5][6][7] propose a closed formula for arbitrary n-point tree amplitudes in a variety of massless quantum field theories.…”