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 (35)

• Modern Theory of Nuclear Forces
• Critical Phenomena and Renormalization-Group Theory
• Supergravity and a Confining Gauge Theory: Duality Cascades and $\chi$SB-Resolution of Naked Singularities
• Low energy hadron physics in holographic QCD
• QCD and a Holographic Model of Hadrons
• Hard Scattering and Gauge/String Duality
• The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
• More on a holographic dual of QCD
• Baryons And Branes In Anti de Sitter Space
• Writing CFT correlation functions as AdS scattering amplitudes
• Resonance Scattering Phase Shifts on a Non-Rest Frame Lattice
• How to go with an RG Flow
• A Natural Language for AdS/CFT Correlators
• The Supergravity Dual of N=1 Super Yang-Mills Theory
• Correlation Functions in Holographic RG Flows
• Holographic Models for QCD in the Veneziano Limit
• Towards Feynman rules for Mellin amplitudes in AdS/CFT
• Conformal Field Theory Correlators from Classical Scalar Field Theory on $Ad{S}_{d+1}$
• Holographic Baryons : Static Properties and Form Factors from Gauge/String Duality
• Exact Results in Non-Supersymmetric Large N Orientifold Field Theories
• Improved Holographic QCD
• Comments on 4-point functions in the CFT/AdS correspondence
• Conformal $n$-point functions in momentum space
• Bulk Phase Shift, CFT Regge Limit and Einstein Gravity
• Breaking the sound barrier in AdS/CFT
• A model of a Fermi liquid using gauge-gravity duality
• Nuclear Force from String Theory
• D-dimensional Conformal Field Theories with anomalous dimensions as Dual Resonance Models
• Towards the higher point holographic momentum space amplitudes II: Gravitons
• Stiff phases in strongly coupled gauge theories with holographic duals
• Glueball Scattering Amplitudes from Holography
• Towards the higher point holographic momentum space amplitudes
• Alternative large Nc baryons and holography
• General aspects of effective field theories and few-body applications
• Baryon Superfluids in AdS/CFT with Flavor

Cited by in corpus (5)

• Unified weak/strong coupling framework for nuclear matter and neutron stars
• Gravitational waves from a holographic phase transition
• Quantum information probes of charge fractionalization in large-$N$ gauge theories
• Scattering length in holographic confining theories
• Revisiting the chiral effective action in holographic models