Chaotic scattering of highly excited strings

Abstract

Motivated by the desire to understand chaos in the S-matrix of string theory, we study tree level scattering amplitudes involving highly excited strings. While the amplitudes for scattering of light strings have been a hallmark of string theory since its early days, scattering of excited strings has been far less studied. Recent results on black hole chaos, combined with the correspondence principle between black holes and strings, suggest that the amplitudes have a rich structure. We review the procedure by which an excited string is formed by repeatedly scattering photons off of an initial tachyon (the DDF formalism). We compute the scattering amplitude of one arbitrary excited string and any number of tachyons in bosonic string theory. At high energies and high mass excited state these amplitudes are determined by a saddle-point in the integration over the positions of the string vertex operators on the sphere (or the upper half plane), thus yielding a generalization of the “scattering equations”. We find a compact expression for the amplitude of an excited string decaying into two tachyons, and study its properties for a generic excited string. We find the amplitude is highly erratic as a function of both the precise excited string state and of the tachyon scattering angle relative to its polarization, a sign of chaos.

Non-negativity of BMN two-point functions with three string modes

“…Our studies thus provide a long term motivation for future research to develop techniques that can deal with string theory on highly curved background, with flux, and including highly excited stringy states, for the purposes of a direct verification of the conjecture (1.6) as well as the complete determination of string amplitudes including the phase angles. Some recent studies concerning highly excited strings are [34,35]. For the moment, our verifications of non-negativity on the gauge theory side provide indirect non-trivial evidence of the conjecture (1.6).…”

From locality to irregularity: Introducing local quenches in massive scalar field theory

“…It is worth noticing that by "chaotic picture" we mean not the exponential growth of the out-of-time-ordered correlators (OTOC), but the erratic behaviour of the energy revivals and oscillations. The notion of the chaotic behaviour in this sense has been studied in quantum mechanics, scattering amplitudes, string theory and two-dimensional CFT, see for example [47][48][49][50][51][52]. It would be interesting to extend this understanding somehow, and we leave this for future research.…”

Chaotic scattering of highly excited strings

“…The study of amplitudes involving more than one excited string is challenging and is largely left to future work; in [42] we compute the simplest amplitude, the three-point amplitude, in which all three strings are excited. 5 , 6…”

“…This is consistent with the Horowitz-Polchinski correspondence as the Hagedorn temperature is 1/ √ α , which coincides with the Bekenstein-Hawking temperature, 1 GM , since G ∼ g 2 s α and M ∼ N/α , which agree when g s ∼ N − 1 4 . Using the methods presented here allows one to compute the exclusive amplitudes of a particular heavy string decaying into a particular heavy string and a photon [42]. Averaging should of course reproduce the blackbody spectrum, but the exclusive amplitude will give much more: it will allow one to see precisely how the radiation differs for each string microstate, the string analog of the long sought goal of extracting information from Hawking radiation.…”

“…The precise function is found by considering all possible Wick contractions involving the creation operators forming the state. The function will be discussed in [42], but we actually don't need to know it. The reason is that in the large N limit the ratio (5.14) is just a number, independent of the angle α.…”