REVIEW
The String Dual of a Confining Four-Dimensional Gauge Theory
High Energy Physics - Theory · Submitted 15 Mar 2000 · 91 references
Pith's verdict: The dielectric 5-brane mechanism is the real contribution and it holds up; the 'quantitatively precise' language in the abstract is doing more work than the q=1, p=1 near-shell geometry can support.
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Referee report
The paper
The paper claims
The paper argues that the supergravity dual of a confining four-dimensional gauge theory is not singular: the D3-branes polarize into five-branes wrapped on a two-sphere, which makes flux-tube tensions, domain walls, baryon vertices and con
The reading
What carries the argument
The mechanism is Myers' dielectric effect transplanted from flat space into AdS: a magnetic Ramond-Ramond three-form flux, dual to the electric seven-form that couples to D3-branes, makes the D3-brane collective coordinates noncommutative and the branes expand into a five-brane wrapping an $S^2$ inside the $S^5$. What makes the calculation tractable is a single small parameter, the ratio of five-brane to D3-brane charge density, $n^2/(gN)$; in that expansion the Born-Infeld and Chern-Simons terms of the probe action nearly cancel, and the surviving potential $-S/V = 4pi g n,|Mvarphi^2 + i zeta m n varphi/12|^2$ turns out to be independent of the warp factor $Z$. That independence is what lets the authors assemble the full set of $N$ branes from probe-sized pieces without the usual factor of one half from charging up, and it is why a highly asymmetric, nonlinear geometry still yields a simple effective potential.
Extended reading notes
Core claim
The central claim is that the supergravity dual of $N=1^*$ is nonsingular in every vacuum because the D3-branes carrying the gauge charge have blown up into five-branes: a single D5-brane for the maximally Higgsed vacuum, an NS5-brane for the confining vacuum, and more generally a collection of $(c,d)$ five-branes whose AdS radii are proportional to their D3 charges, $z_I = pi alpha' i m n_I/(M_I sqrt{2})$. The confining flux tube is then a fundamental string bound to the NS5-brane, with tension $tau_e = m^2 gN/2$; the magnetic flux tube of the Higgs vacuum is a D-string bound to the D5-brane, with $tau_m = m^2 N/(2g)$. The baryon vertex is a D3-brane filling the three-ball whose boundary is the five-brane's two-sphere, and a domain wall is a triple five-brane junction whose tension reproduces the field-theory superpotential difference. The paper also addresses the apparent overcounting of brane configurations, in which $p$ D5-branes of charge $q$ and $q$ NS5-branes of charge $p$ would describe the same vacuum: their validity conditions $qg/p gg 1$ and $gp/q gg 1$ are complementary, so only one description ever lies inside the supergravity regime.
Load-bearing premise
The load-bearing premise is that the five-brane charge is a small perturbation of an $N=4$ Coulomb-branch configuration, valid only when $n^2/(gN)gg 1$; the paper concedes that this expansion must break down near the five-brane shell and repairs it only by matching onto a flat D5+D3 solution with an order-one constant left undetermined.
Editorial extensions
If this is right
- Condensates of dimension-three operators become calculable, because the normalizable $1/r^3$ mode of $G_3$ is fixed by the brane source instead of being left free by a naked singularity.
- Domain-wall tensions follow from a triple five-brane junction and match the field-theory superpotential difference, for example $tau_{DW} approx |m^3| g^2 N^3/(24 pi)$ between the confining and first oblique confining vacua.
- The large-$N$ instanton expansion is reorganised: the second Eisenstein series term $E_2(tau/N)$ becomes an expansion in $e^{-2pi gN}$, realised as a string worldsheet wrapping the NS5-brane two-sphere with area times tension $2pi gN$.
- Baryons become finite-size objects, a D3-brane filling the ball bounded by the five-brane sphere with mass of order $Nm sqrt{gN}$ and $N$ fundamental strings ending on it, which explains why flux tubes carry only $Z_N$ charge.
- The construction extends to the nonsupersymmetric case by adding a fourth mass, and to orbifolds giving QCD-like theories with heavy quarks in which flux tubes are only metastable.
Reading between the lines
- If the same polarization mechanism applies to any relevant perturbation that turns on a three-form flux, then the repulson-type singularities of $N=2$ duals and the incipient throat of Randall-Sundrum compactifications are capped by the same kind of expanded brane, which would unify several separate singularity-resolution stories under one mechanism.
- The discreteness of the normalizable coefficients, fixed by the brane source rather than free, is a direct argument against reading arbitrary singular supergravity solutions as legitimate states, which is the assumption behind proposals that integrate inward past a singularity to obtain a small cosmological constant.
- The undetermined matching constant in the crossover radius cancels out of the flux-tube tension, which suggests the correspondence-principle matching between the supergravity and brane-field-theory descriptions may be exact for BPS quantities even where neither description is valid in between; the same check has not been done for the baryon mass.
- Because only one of the D5 and NS5 descriptions is in range at a time, the crossover itself is a strong-coupling brane transition that supergravity cannot see, and the noncommutative gauge theory on the five-brane is the natural setting in which to look for it.
Original abstract
We study N=1 gauge theories obtained by adding finite mass terms to N=4 Yang-Mills theory. The Maldacena dual is nonsingular: in each of the many vacua, there is an extended brane source, arising from Myers' dielectric effect. The source consists of one or more (p,q) 5-branes. In particular, the confining vacuum contains an NS5-brane; the confining flux tube is a fundamental string bound to the 5-brane. The system admits a simple quantitative description as a perturbation of a state on the N=4 Coulomb branch. Various nonperturbative phenomena, including flux tubes, baryon vertices, domain walls, condensates and instantons, have new, quantitatively precise, dual descriptions. We also briefly consider two QCD-like theories. Our method extends to the nonsupersymmetric case. As expected, the N=4 matter cannot be decoupled within the supergravity regime.
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
We study N=1 gauge theories obtained by adding finite mass terms to N=4 Yang-Mills theory. The Maldacena dual is nonsingular: in each of the many vacua, there is an extended brane source, arising from Myers' dielectric effect. The source consists of one or more (p,q) 5-branes. In particular, the confining vacuum contains an NS5-brane; the confining flux tube is a fundamental string bound to the 5-brane. The system admits a simple quantitative description as a perturbation of a state on the N=4 Coulomb branch. Various nonperturbative phenomena, including flux tubes, baryon vertices, domain walls, condensates and instantons, have new, quantitatively precise, dual descriptions. We also briefly consider two QCD-like theories. Our method extends to the nonsupersymmetric case. As expected, the N=4 matter cannot be decoupled within the supergravity regime.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We study N=1 gauge theories obtained by adding finite mass terms to N=4 Yang-Mills theory. | contribution 0.85 | 0.80 | 0.04 | asserted 0.97 |
| s1 | The Maldacena dual is nonsingular: in each of the many vacua, there is an extended brane source, arising from Myers' dielectric effect. | result 1.00 | 0.80 | 0.37 | asserted 1.00 |
| s2 | The source consists of one or more (p,q) 5-branes. | result 0.99 | 0.71 | 0.10 | asserted 1.00 |
| s3 | In particular, the confining vacuum contains an NS5-brane; the confining flux tube is a fundamental string bound to the 5-brane. | result 0.99 | 0.80 | 0.27 | asserted 1.00 |
| s4 | The system admits a simple quantitative description as a perturbation of a state on the N=4 Coulomb branch. | method 0.72 | 0.74 | 0.10 | asserted 0.97 |
| s5 | Various nonperturbative phenomena, including flux tubes, baryon vertices, domain walls, condensates and instantons, have new, quantitatively precise, dual descriptions. | result 0.88 | 0.84 | 0.26 | asserted 0.99 |
| s6 | We also briefly consider two QCD-like theories. | contribution 0.93 | 0.73 | 0.02 | asserted 0.91 |
| s7 | Our method extends to the nonsupersymmetric case. | contribution 0.47 | 0.68 | 0.06 | asserted 0.97 |
| s8 | As expected, the N=4 matter cannot be decoupled within the supergravity regime. | limitation 0.78 | 0.43 | 0.07 | asserted 0.97 |
What was examined, and what was not
- arXiv listing abstract v2
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- P abstract
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Figures
Figures reproduced from arXiv:hep-th/0003136 by the authors.
References
How later papers used it
158 later papers cite it
1 later paper by other authors is listed below: 1 used its method or tool.
Uses its method or tool 1 of 5 papers with this label
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Followed this paper in modeling a magnetic vortex as a D1-brane probe in this geometry.
Non-Abelian k-Vortex Dynamics in N=1^* theory and its Gravity Dual (2008) · 0.92 · paraphrased: the licence does not allow quoting
How the literature uses it
159 arXiv papers cite this in 316 sentences
Papers citing it · 217 sentences without a confident label
Contests it 1 paper
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Only the choice we have made leads to the correct potential for antibrane decay, however; the opposite choice can be seen to lead to a potential that gains energy by adding antibrane charge.] [equation] The field strength for $F_3$ can be realized from the potential [equation] where $θ$ and $ϕ$ parameterize the two-sphere, while the six-form potentials may be obtained from [ref] [equation] and thus may be chosen to vanish.[In [ref] the WZ contribution to the potential was stated to be obtained from $B_6$, but this is zero; the relevant term actually comes from $C_4 ∧F_2$.]
Brane/flux annihilation transitions and nonperturbative moduli stabilization · Life and decay of antibranes · contest 0.79
Builds on it 1 paper
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This result was later extended in [ref] to include all the massive vacua and arrive at the following IR effective superpotential
A Holographic Kaleidoscope for $\mathcal{N}=1^*$ · Vacua of $=1^*$ · 0.96
Uses its method or tool 5 papers
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To this end we will introduce a three-form flux $G_3 = F_3 - τH_3$ in the type IIB background following [ref] . $F_3$ and $H_3$ are RR and NSNS three-form fluxes.
GMOR relation for a QCD-like theory from S-duality · GMOR relations from S-duality · 0.98
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Following [ref] , we model a magnetic vortex as a D1-brane probe in this geometry.
Non-Abelian k-Vortex Dynamics in N=1^* theory and its Gravity Dual · The Vortex as a D1-brane · 0.92
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This was done by implementing two different setups for holography, i.e., the hard- [ref] and the soft-wall [ref] models.
Linear confinement without dilaton in bottom-up holography for walking technicolour · Introduction · 0.91
Compares with it 15 papers
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In section two we study the first order phase transition dynamics of Polchinski-Strassler's model [ref] , often called hard wall model, and we get a similar conclusion as that of Horowitz and Roberts [ref] .
Phase Transition Dynamics and Its Alpha' Corrections · Introduction · 0.94
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We use the Einstein frame of [ref] , $g_μν^PS = g_s^1/2 e^-Φ/2 g_μν^string$, while the authors of [ref] use $g_μν^ABY = e^-Φ/2 g_μν^string$, so the metric we use here is related to theirs by $g_μν = g_s^1/2 g_μν^ABY$.
A Gravity Dual of Metastable Dynamical Supersymmetry Breaking · Appendix D: Matching to ABY Solutions · 0.85
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Our matched asymptotic expansion scheme shares certain qualitative features with the interpolating metric proposed in [ref] , though the crucial difference is that here the matching is by construction in agreement with the supergravity equations, including all the supergravity fields.
Holographic duals of the $\mathcal{N}=1$* gauge theory · Polchinski-Strassler vacua · 0.97
Cites it as support 5 papers
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More evidence in support of this possibility was offered in [ref] .
Non-Abelian k-Vortex Dynamics in N=1^* theory and its Gravity Dual · The Vortex as a D1-brane · 1.00
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As mentioned earlier this is motivated by the work of [ref] .
Can the Hagedorn Phase Transition be explained from Matrix Model for Strings? · Review of Super-gravity Results · 0.96
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Since the axion-dilaton system naturally couples to fluxes, the well-known eponymous string theory results [ref] corroborate the discreteness of the configurations [ref], as do the general string theory expectations [ref] ; however, we are not aware of a rigorous proof.
On Stringy de Sitter Spacetimes · Viability and Features · 0.99
Cites it as background 49 papers
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The string theory dual of $N=1^*$ theory was constructed by Polchinski and Strassler [ref] by considering an appropriate deformation of Type IIB string theory on $AdS_5×S^5$ background.
Non-Abelian k-Vortex Dynamics in N=1^* theory and its Gravity Dual · The Vortex in the String Dual · 0.96
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In [ref] , Polchinski and Strassler proposed another interesting phenomenological model by removing the small radius region of AdS which corresponds to introducing an IR cutoff in the dual conformal field theory.
Phase Transition Dynamics and Its Alpha' Corrections · Introduction · 0.93
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A particularly interesting example for a supergravity background was discussed by Polchinski and Strassler [ref] .
Holographic flavour in the N=1 Polchinski-Strassler background · Introduction · 0.96
Discussion
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