REVIEW
The domain-wall/QFT correspondence
High Energy Physics - Theory · Submitted 20 Jul 1998 · 40 references
Pith's verdict: A useful framework paper: the dual-frame trick makes the near-horizon geometry of every Dp-brane non-singular and hands you the effective gauged supergravity, but the advertised R-symmetry check is automatic and the p=5,6 cases are left open.
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Referee report
The paper
The paper claims
The paper argues that the anti-de Sitter/conformal-field-theory correspondence is one case of a wider rule: a gauged supergravity whose vacuum is a half-supersymmetric domain wall is dual to the quantum field theory living on that wall.
The reading
What carries the argument
The load-bearing device is the dual-frame metric, $g^{dual} = (e^{i} N)^{2/(p-7)} g^{st}$, defined so that the tension of the dual $(6-p)$-brane is dilaton-independent. In this frame the Dp-brane solution's near-horizon limit is non-singular and factorizes as $ds^2 = u^2 R^2 ds^2( E^{(p,1)}) + R^2 du^2/u^2 + dOmega^2_{(8-p)}$ with a linear dilaton, where $R = 2/(5-p)$ is the anti-de Sitter radius. Rewriting the resulting effective action in the Einstein frame turns the linear-dilaton anti-de Sitter vacuum into a domain wall of the form studied by Lü, Pope and Townsend, characterized by the parameter $Delta = a^2 - 2(D-1)/(D-2) = -4(7-p)/(9-p)$, which equals the anti-de Sitter value only at $p=3$. The exponent $a$ in the dilaton potential, and hence the whole shape of the wall, is fixed by $p$ alone; the compactification sphere then supplies the gauge group, and the gauge group is what must match the R-symmetry of the wall's field theory.
Extended reading notes
Core claim
The central claim is that a gauged supergravity theory whose vacuum is a half-supersymmetric domain wall is dual to the quantum field theory on that domain wall, in the same sense that an anti-de Sitter supergravity is dual to a conformal field theory on its boundary. The authors establish the correspondence case by case: for each Dp-brane ($p=0,1,2,4,5,6$) they take the near-horizon limit in the dual frame, read off the sphere compactification, and identify the effective lower-dimensional gauged supergravity together with its gauge group. The list runs from an $S^8$ compactification of IIA supergravity to $D=2$ $SO(9)$ gauged maximal supergravity, through $S^7$ to $D=3$ $SO(8)$, $S^6$ to $D=4$ $ISO(7)$ gauged $N=8$, $S^4$ to $D=6$ $SO(5)$, $S^3$ to $D=7$ $SU(2)$, and $S^2$ to $D=8$ $SU(2)$ — the last being the Salam–Sezgin theory, whose dilaton potential the authors show matches the gravity/dilaton sector they derive. In every case the supergravity gauge group coincides with the R-symmetry group of the corresponding worldvolume field theory, which is the paper's main consistency test. A second, independent observation is that the radial coordinate of the dual-frame metric is precisely the holographic energy scale of the boundary theory, so the dual frame is the natural 'holographic frame' in which to read off the energy–distance relation.
Load-bearing premise
The construction assumes that the dual-frame near-horizon geometry is a genuine gravity dual of the decoupled worldvolume theory for every $p$; the authors themselves note that at $p=6$ the supergravity description and weakly coupled Yang–Mills appear valid in the same region, which 'would seem to lead to a contradiction', and that the $p=5$ case is awkward because Minkowski space has no boundary.
Editorial extensions
If this is right
- Every Dp-brane with $p \le 6$ acquires a candidate gravity dual, not just the conformal $p=3$ case, with the dual's gauge group fixed by the brane's R-symmetry group.
- The $SU(2)$-gauged maximal $D=8$ supergravity of Salam and Sezgin gains a brane interpretation, as the near-horizon limit of the IIA D6-brane, and its domain wall solution is shown to be half-supersymmetric using its own transformation rules.
- The $ISO(7)$-gauged $N=8$ theory in $D=4$ is identified as the effective theory of the D2-brane, opening a $CSO(8-k,k)$ series from toroidal reductions of the M2-brane.
- The choice of horosphere in the domain-wall spacetime corresponds to a choice of coupling constant in the boundary theory, so moving along the wall interpolates between weak and strong coupling rather than between vacua of a conformal theory.
- The dual frame is argued to be the frame in which the radial coordinate equals the holographic energy scale, giving a uniform energy–distance relation across all $p$.
Reading between the lines
- If the gauge-group/R-symmetry matching is the real test, then the prediction is sharpest where the candidate bulk theory does not yet exist: the paper flags an $ISO(4)$-gauged $D=7$ maximal supergravity and an $SO(4)$-gauged $D=7$ theory as missing, and those are exactly the cases where the matching can be used to constrain model-building rather than merely confirm it.
- The observation that the dual frame carries the holographic energy scale suggests a reading the authors do not pursue: the frame choice is not a calculational convenience but a statement about which metric probes which scales, so a boundary observer's renormalization group flow may be geometrically represented by a change of frame rather than by motion in a fixed one.
- Because the domain-wall parameter $\Delta$ depends only on $p$, the family of duals is discrete; a natural extension is to ask whether the interpolating solutions between different $p$ (the intersecting-brane cases the authors defer) correspond to flows between the associated field theories.
Original abstract
We extend the correspondence between adS-supergravities and superconformal field theories on the adS boundary to a correspondence between gauged supergravities (typically with non-compact gauge groups) and quantum field theories on domain walls.
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 extend the correspondence between adS-supergravities and superconformal field theories on the adS boundary to a correspondence between gauged supergravities (typically with non-compact gauge groups) and quantum field theories on domain walls.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We extend the correspondence between adS-supergravities and superconformal field theories on the adS boundary to a correspondence between gauged supergravities (typically with non-compact gauge groups) and quantum field theories on domain walls. | contribution 1.00 | 0.89 | 0.79 | asserted 1.00 |
What was examined, and what was not
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Figures
Figures reproduced from arXiv:hep-th/9807137 by the authors.
References
How the literature uses it
78 arXiv papers cite this in 132 sentences
Papers citing it · 83 sentences without a confident label
Builds on it 1 paper
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In this section we generalize the discussion of the scaling similarity transformation for the near horizon geometries describing all $Dp$ branes [ref] , see also [ref] .
Scaling similarities and quasinormal modes of D0 black hole solutions · Other Dp brane geometries · 0.86
Uses its method or tool 1 paper
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Nevertheless it is possible to use the results in [ref] to evaluate the on-shell action of the spherical brane solutions and reproduce the scaling of the free energy with $N$ and $λ_eff$ in [ref].
Spherical Branes · Introduction · 0.95
Compares with it 2 papers
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For $d=8$, this reproduces the half-supersymmetric domain wall solution of [ref] , corresponding to the ten-dimensional D0-brane near-horizon geometry.
Consistent sphere reductions of gravity to two dimensions · $SO(d+1)$ invariant solution · 0.98
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As pointed out in [ref] , this consistent reduction on $S^2$ is the same as the conventional Scherk–Schwarz reduction of eleven-dimensional supergravity on the group manifold $(2)≃S^3$, presented long ago in [ref] .
Exceptional generalised geometry for massive IIA and consistent reductions · $S^2$ parallelisation and $D=8$, $(3)$ supergravity · 0.80
Cites it as background 42 papers
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This goes by the name “Domain Wall/QFT correspondence" [ref] .[Henceforth labeled “DW/QFT" for short.] The fact that the metric ([ref]) is conformal to AdS can be phrased as crucial to the duality, which was established by decoupling the near-horizon dynamics of non-conformal D-branes: passage to a conformal, so-called “dual" frame in which the D-brane near-horizon metric becomes AdS$_p+2×S^8-p$ reveals a manifest $(p+2)$-dimensional gravitational description, in which we identify the radial direction with the energy scale of the dual field theory [ref] .
Domain Wall Holography for Finite Temperature Scaling Solutions · Introduction and summary · 0.90
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The project of extending the original duality to theories with a renormalization-group flow was initiated in [ref] and many different lines of research were proposed to compute non-perturbative effects in quantum field theories with small amount of Supersymmetry (SUSY).
Comments on the String dual to N=1 SQCD · Introduction · 0.96
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The relation between the energy scale in a non-conformal SYM theory and the “radial coordinate” in a dual supergravity background is a subtle problem that has been discussed in a similar context in [ref] .
Spherical Branes · Holographic interpretation · 0.87
Discussion
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