REVIEW
Nonlocal Field Theories and their Gravity Duals
High Energy Physics - Theory · Submitted 13 Mar 2001 · 62 references
Pith's verdict: The geometric core — an explicit dipole gravity dual whose boundary metric degenerates along the dipole direction — is solid and worth citing; the type-0A UV story is a conjecture the authors themselves label as one.
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Referee report
The paper
The paper claims
Dipole theories — nonlocal field theories whose fields carry a fixed-length dipole vector — have gravity duals whose metric degenerates at the boundary, and T-dualizing the degenerate circle turns the dipole length into a string-scale short
The reading
What carries the argument
The load-bearing construction is the chain of T-dualities around a compactified direction with a transverse $SO(6)$ twist inserted between them, together with the Hopf-fibration description of the deformed $S^5$. The twist is what encodes the dipole vectors: a string worldsheet with winding $w_j$ and $Z$-charge $q_j$ picks up a phase $e^{iα∑_{i<j} w_i q_j}$, which reproduces the dipole phase $e^{i∑_{i<j} p_i L_j}$ once $L_j = α'α q_j/R_3$ and $p_j = R_3 w_j/α'$. Writing the deformed sphere in Hopf coordinates makes the $U(3)$ symmetry manifest, keeps the $ℂP^2$ metric fixed, and isolates the shrinking fiber whose radius $ρ(u)$ controls where supergravity stops being trustworthy, at $u ∼ λ^{1/2}L̃$.
Extended reading notes
Core claim
For a dipole deformation of $N=4$ super-Yang-Mills with all dipole vectors along one direction and equal magnitude, the authors derive the ten-dimensional string-frame metric and find that the internal $S^5$ degenerates as the boundary $u→0$ is approached. The sphere retains the structure of an $S^1$ Hopf fibration over $ℂP^2$ with a constant-volume base, but the fiber radius is $ρ(u) = R u/√(u^2+λ^2 L̃^2)$, so the fiber collapses while the base does not. T-dualizing the fiber gives a type-IIA metric in which the field-theory direction $x^3$ is fibered over a circle of radius $α'R$: the proper distance between $(x^3,γ)$ and $(x^3+2πL̃,γ)$ is only of string scale, while the distance between generic nearby $x^3$ points diverges as $u→0$. The nonlocality of the field theory is thus literally a shortcut through an extra dimension, and the four-dimensional conformal group is restored for the combination $x^3+L̃γ$. A second strand of the paper is a puzzle and its proposed resolution: fermions carry dipole lengths $±L/2$ and $±3L/2$, which no closed Wilson line can match, and the authors argue that the fermions are anti-periodic around the Hopf fiber, so the correct T-duality includes $(-)^F$ and produces type-0A string theory with a strong RR flux rather than type-IIA.
Load-bearing premise
The resolution of the fermion puzzle assumes that T-duality with a $(-)^F$ twist yields a weakly coupled type-0A theory with a strong RR flux in which the tachyon is absent; the authors flag both that quantizing strings in strong RR backgrounds is an open problem and that type-0A likely has a large cosmological constant.
Editorial extensions
If this is right
- Nonlocality in a field theory with a fundamental length shows up as degeneracy of the dual metric on the boundary, not as a modification of the four-dimensional part of the geometry.
- The dipole length $L = 2πL̃$ becomes a topological identification of boundary points through a T-dual circle, giving a concrete geometric picture of why separated fields interact.
- The internal sphere's isometries are broken from $Spin(6)$ to $U(3)$, and the resulting metric perturbations map onto specific operators of dimension 5 and 6 in the dual field theory, matching the expected dipole deformation.
- The ultraviolet of these theories is conjecturally described by type-0A string theory with a strong RR field strength, so a single field theory interpolates between type-IIB and type-0 string descriptions along the renormalization group flow.
- Correlation functions of zero-dipole operators acquire a mass-like term $mR = λ k_3 L̃$, producing oscillations in momentum space at a scale set by $λL̃$.
Reading between the lines
- The paper's own correlator result oscillates at $λL̃$ rather than at the dipole length $L̃$; if that is not a supergravity artifact, the geometric shortcut and the field-theory nonlocality are offset by a factor of the 't Hooft coupling, which would be a sharp and checkable discrepancy between the two sides.
- The same Hopf-fiber degeneration should occur for any dipole deformation whose dipole matrix has equal eigenvalues, so the construction suggests a general diagnostic: compute the fiber radius as a function of the radial coordinate and read off the nonlocality scale directly.
- The proposed type-0A resolution predicts no tachyon because the RR flux shifts its mass; a worldsheet computation of the winding-state mass in the presence of the five-form flux would decide whether the ultraviolet picture is consistent.
- The authors note in the discussion that the analogous construction for the six-dimensional $(2,0)$ theory would involve constant-area 'discpoles' with an $AdS_7×S^4$ dual, which is a natural next test of whether the degeneration mechanism is generic.
Original abstract
The gravity duals of nonlocal field theories in the large N limit exhibit a novel behavior near the boundary. To explore this, we present and study the duals of dipole theories - a particular class of nonlocal theories with fundamental dipole fields. The nonlocal interactions are manifest in the metric of the gravity dual and type-0 string theories make a surprising appearance. We compare the situation to that in noncommutative SYM.
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
The gravity duals of nonlocal field theories in the large N limit exhibit a novel behavior near the boundary. To explore this, we present and study the duals of dipole theories - a particular class of nonlocal theories with fundamental dipole fields. The nonlocal interactions are manifest in the metric of the gravity dual and type-0 string theories make a surprising appearance. We compare the situation to that in noncommutative SYM.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The gravity duals of nonlocal field theories in the large N limit exhibit a novel behavior near the boundary. | background 0.63 | 0.32 | 0.41 | asserted 1.00 |
| s1 | To explore this, we present and study the duals of dipole theories - a particular class of nonlocal theories with fundamental dipole fields. | contribution 0.99 | 0.92 | 0.07 | asserted 0.93 |
| s2 | The nonlocal interactions are manifest in the metric of the gravity dual and type-0 string theories make a surprising appearance. | result 0.99 | 0.81 | 0.30 | asserted 1.00 |
| s3 | We compare the situation to that in noncommutative SYM. | contribution 0.60 | 0.72 | 0.04 | unclear 0.60 |
What was examined, and what was not
- arXiv listing abstract v4
- full text
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- P abstract
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Figures
Figures reproduced from arXiv:hep-th/0103090 by the authors.
References
How the literature uses it
35 arXiv papers cite this in 52 sentences
Papers citing it · 33 sentences without a confident label
Uses its method or tool 2 papers
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This procedure was applied in [ref] to obtain the corresponding gravity solutions.
Comments on string theory backgrounds with non-relativistic conformal symmetry · DLCQ of the dipole theory and its gravity dual · 0.86
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To produce these solutions, we will use a solution-generating technique called the Null Melvin Twist [ref] , which we will review in detail below.
Hot Spacetimes for Cold Atoms · Introduction · 1.00
Cites it as background 15 papers
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Interesting examples involve the so-called $β$ [ref] , noncommutative [ref] and dipole deformations [ref] of $=4$ SYM, in which the corresponding dual gravity backgrounds are identified with so-called TsT transformations (a succession of T-duality, shift and T-duality along $U(1) ×U(1)$ isometries) of the original geometry (for an overview see [ref] ).
TsT, $T\bar{T}$ and black strings · Introduction · 0.86
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Asymptotically Schrödinger spacetimes with four noncompact dimensions [ref] can be embedded in string theory [ref] by applying to asymptotically $AdS_5×X_5$ solutions in type IIB string theory a solution-generating technique known as the Null Melvin Twist [ref] .
Stability of Asymptotically Schroedinger RN Black Hole and Superconductivity · Introduction · 0.83
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Its deformations include: noncommutative Yang-Mills where the Neveu-Shwarz two form is present along the brane world volume [ref] ; the so called dipole theory where the Neveu-Schwarz two form is present with one leg along the brane world volume and one off it [ref] ; and finally the $𝒩=1$ $β$-deformed Yang-Mills theory where the Neveu Schwarz two form is present entirely off the brane world volume [ref] .
M-Theory Brane Deformations · Introduction · 0.92
Discussion
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