Scattering length from holographic duality

Abstract

Interesting theories with short range interactions include QCD in the hadronic phase and cold atom systems. The scattering length in 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 $\Delta >d/4$. For $d<4$ this is more stringent than the unitarity constraint and may be applicable to an extended family of large-$N$ theories with a discrete spectrum of massive states. We also argue that for scalar potentials with polynomial terms of order $K$, a constraint more restrictive than the unitarity bound will appear for $d<2K/(K-2)$.

17 pages, 4 figures

References in corpus (7)

• Writing CFT correlation functions as AdS scattering amplitudes
• Improved Holographic QCD
• Breaking the sound barrier in AdS/CFT
• D-dimensional Conformal Field Theories with anomalous dimensions as Dual Resonance Models
• Stiff phases in strongly coupled gauge theories with holographic duals
• Alternative large Nc baryons and holography
• Baryon Superfluids in AdS/CFT with Flavor