REVIEW
Gauge/string duality and scalar glueball mass ratios
High Energy Physics - Theory · Submitted 17 Dec 2002 · 21 references
Pith's verdict: A clean four-page hard-wall calculation with correct Bessel-zero arithmetic; the derivation route is the real contribution, and the 'good agreement' line is oversold for 3d.
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Referee report
The paper
The paper claims
Scalar glueball mass ratios come out as ratios of zeros of a Bessel function, with no dependence on where the anti-de Sitter slice is cut off.
The reading
What carries the argument
The mechanism is the discretisation of a bulk field by a boundary condition. Putting the dilaton in a finite AdS slice and demanding it vanish at the infrared wall turns a continuous momentum into a discrete tower indexed by the zeros of the Bessel function $J_2$; the physical input is the assumption that each discrete momentum is proportional to a glueball mass, so the zeros themselves become the mass ratios. The choice of Dirichlet rather than Neumann conditions is what fixes the Bessel order and hence the specific numbers.
Extended reading notes
Core claim
The claim is that the mass ratios of the scalar glueball $0^{++}$ and its excitations are the ratios of the zeros of a Bessel function. Working in an AdS$_5$ slice $0<z<z_{max}$, the authors expand the free dilaton field in modes $z^2 J_2(u_p z)$ with a Dirichlet condition at $z=z_{max}$, which quantises the momenta as $u_p = chi_{2,p}/z_{max}$ where $J_2(chi_{2,p})=0$. Identifying the slice size with the inverse mass of the lightest glueball, $z_{max}=C/mu_1$, and assuming the glueball masses are proportional to the discrete dilaton momenta, they obtain $mu_p/mu_1 = chi_{2,p}/chi_{2,1}$. The same construction in one lower dimension, with $J_{3/2}$ in place of $J_2$, gives the three-dimensional ratios. Because the slice size cancels in the ratio, the predicted spectrum contains no adjustable parameter beyond the overall scale, and the authors present it side by side with lattice and black-hole supergravity numbers in two tables.
Load-bearing premise
The step that carries the result is the assumption that each glueball mass is proportional to the corresponding discrete dilaton momentum, a relation the paper says is suggested by the correspondence but does not derive.
Editorial extensions
If this is right
- Once the lightest scalar glueball mass is known, the whole tower of scalar excitations is predicted with no further input: $1.61$, $2.64$, $3.64$, $4.64$, $5.63$, $6.62$ GeV in the four-dimensional case.
- The same recipe transfers to three-dimensional confining theories by changing the Bessel order to $J_{3/2}$, giving ratios that track the lattice values there as well.
- Because the ratios are independent of the slice size, the construction is insensitive to how the infrared cutoff is chosen, which removes one free knob from the model.
- The method is not specific to glueballs: any strongly interacting state dual to a bulk field with a definite boundary condition should get a spectrum from the same zero-finding exercise.
Reading between the lines
- The paper's own tables show the agreement weakening with excitation number: the third and fourth states come out at $3.64$ and $4.64$ against $3.11$ and $3.82$ from black-hole supergravity, so the scheme looks like a good first approximation that drifts for higher modes.
- The Dirichlet condition is doing most of the quantitative work; a Neumann or mixed condition would give a different Bessel order and a different tower, so a natural extension is to ask which boundary condition the dual field theory actually dictates.
- Because the ratios are pure numbers fixed by Bessel zeros, a precise lattice determination of the third and fourth scalar glueball masses would be enough to discriminate this model from the black-hole supergravity one without needing the absolute scale.
- The same logic could be turned around: if a confining theory's low-lying spectrum were known, the pattern of Bessel zeros it matches would say something about the effective dimensionality and boundary condition of its dual geometry.
Original abstract
It has been shown by Polchinski and Strassler that the scaling of high energy QCD scattering amplitudes can be obtained from string theory. They considered an AdS slice as an approximation for the dual space of a confining gauge theory. Here we use this approximation to estimate in a very simple way the ratios of scalar glueball masses imposing Dirichlet boundary conditions on the string dilaton field. These ratios are in good agreement with the results in the literature. We also find that they do not depend on the size of the slice.
The compiled record
The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
The abstract, sentence by sentence
It has been shown by Polchinski and Strassler that the scaling of high energy QCD scattering amplitudes can be obtained from string theory. They considered an AdS slice as an approximation for the dual space of a confining gauge theory. Here we use this approximation to estimate in a very simple way the ratios of scalar glueball masses imposing Dirichlet boundary conditions on the string dilaton field. These ratios are in good agreement with the results in the literature. We also find that they do not depend on the size of the slice.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | It has been shown by Polchinski and Strassler that the scaling of high energy QCD scattering amplitudes can be obtained from string theory. | background 1.00 | 0.02 | 0.03 | asserted 1.00 |
| s1 | They considered an AdS slice as an approximation for the dual space of a confining gauge theory. | background 0.96 | 0.06 | 0.03 | asserted 1.00 |
| s2 | Here we use this approximation to estimate in a very simple way the ratios of scalar glueball masses imposing Dirichlet boundary conditions on the string dilaton field. | contribution 0.62 | 0.96 | 0.23 | asserted 0.95 |
| s3 | These ratios are in good agreement with the results in the literature. | result 0.85 | 0.71 | 0.34 | asserted 0.93 |
| s4 | We also find that they do not depend on the size of the slice. | result 1.00 | 0.96 | 0.19 | asserted 1.00 |
What was examined, and what was not
- arXiv listing abstract v2
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- references and citing sentences
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- P abstract
- S sections
- T body sentences
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- R cross-paper relations
References
How the literature uses it
80 arXiv papers cite this in 102 sentences
Papers citing it · 46 sentences without a confident label
Contests it 2 papers
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However neither the hard wall [ref] , the soft wall [ref] or the D4-D8 [ref] models provide decay constants decreasing with excitation level.
Heavy meson dissociation in a plasma with magnetic fields · Introduction · contest 0.72
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The original bottom up holographic models, like the precursor hard wall model [ref] , provide decay constants that behave inconsistently with the experimental results.
Quasinormal modes for quarkonium in a plasma with magnetic fields · AdS/QCD description of heavy vector mesons · contest 0.75
Uses its method or tool 1 paper
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The dynamics and interactions of baryons and vector mesons are described using the AdS/QCD hard wall model [ref] .
Holographic model for dilepton production in p-p collisions · Introduction · 0.96
Compares with it 8 papers
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This result, in appropriate units, is of the same order of magnitude as the real Coulombic term obtained by comparing with Charmonium spectra as first modelled by [ref] and subsequently by several authors [ref] - [ref] , [ref] - [ref] , [ref] - [ref] .
From string theory to large N QCD · Quark-Anti quark potential for small $u_max$ · 0.98
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This result is consistent with previous results presented in the literature, where the Regge trajectory for vector and axial-vector mesons was found to exhibit asymptotic quadratic behavior $λ_n ∼n^2$ in the $D4-D8$ model [ref] , the hard-wall model [ref] and the $D3-D7$ model [ref] .
Pion and Vector Meson Form Factors in the Kuperstein-Sonnenschein holographic model · Results · 0.95
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Such behaviour is similar to the ones found in hard-wall model [ref] and the D3-D7 brane model [ref] .
Form factors of vector and axial-vector mesons in holographic D4-D8 model · Wave functions and Regge trajectories · 1.00
Cites it as background 37 papers
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In particular these dualities lead to some holographic models to describe non perturbative aspects of QCD known as AdS/QCD (see for instance [ref] ).
Holographic model for dilepton production in p-p collisions · Introduction · 0.86
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The holographic hard wall model (HW) [ref] introduces a hard cutoff in the AdS space, described by Poincaré coordinates
Anomalous and Linear Holographic Hard Wall Models for Glueballs and the Pomeron · Introduction · 0.93
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Work along these lines has become very popular in the past couple of years; especially well represented and close to this work in spirit are studies of hadronic spectra [ref] , the couplings of hadrons in the presence of chiral symmetry breaking [ref] , and hadronic form factors [ref] .
Pion Form Factors in Holographic QCD · Introduction · 0.87
Discussion
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