Abstract
Interesting theories with short range interactions include QCD in the hadronic phase and cold atom systems. The scattering length in a two-to-two elastic scattering process captures the most elementary features of the interactions, such as whether they are attractive or repulsive. However, even this basic quantity is notoriously difficult to compute from first principles in strongly coupled theories. We present a method to compute the two-to-two amplitudes and the scattering length using the holographic duality. Our method is based on the identification of the residues of Green’s functions in the gravity dual with the amplitudes in the field theory. To illustrate the method we compute a contribution to the scattering length in a hard wall model with a quartic potential and find a constraint on the scaling dimension of a scalar operator . For this is more stringent than the unitarity constraint and may be applicable to an extended family of large- theories with a discrete spectrum of massive states. We also argue that for scalar potentials with polynomial terms of order , a constraint more restrictive than the unitarity bound will appear for .
- Received 11 November 2019
- Accepted 5 February 2020
DOI:https://doi.org/10.1103/PhysRevD.101.046028
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.
Published by the American Physical Society