A planar diagram theory for strong interactions

doi:10.1016/0550-3213(74)90154-0

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A planar diagram theory for strong interactions

Journal Article•DOI•

A planar diagram theory for strong interactions

Gerard 't Hooft¹•Institutions (1)

CERN¹

18 Apr 1974-Nuclear Physics (Elsevier)-Vol. 72, Iss: 3, pp 461-473

TL;DR: In this article, it was shown that only planar diagrams with the quarks at the edges dominate; the topological structure of the perturbation series in 1/N is identical to that of the dual models, such that the number 1/n corresponds to the dual coupling constant.

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About: This article is published in Nuclear Physics.The article was published on 1974-04-18 and is currently open access. It has received 4449 citations till now. The article focuses on the topics: 1/N expansion & Gauge group.

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Journal Article•DOI•

Anti De Sitter Space And Holography

[...]

Edward Witten

20 Feb 1998-Advances in Theoretical and Mathematical Physics

TL;DR: In this article, it was shown that the Kaluza-Klein modes of Type IIB supergravity on $AdS_5\times {\bf S}^5$ match with the chiral operators of the super Yang-Mills theory in four dimensions.

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Abstract: Recently, it has been proposed by Maldacena that large $N$ limits of certain conformal field theories in $d$ dimensions can be described in terms of supergravity (and string theory) on the product of $d+1$-dimensional $AdS$ space with a compact manifold. Here we elaborate on this idea and propose a precise correspondence between conformal field theory observables and those of supergravity: correlation functions in conformal field theory are given by the dependence of the supergravity action on the asymptotic behavior at infinity. In particular, dimensions of operators in conformal field theory are given by masses of particles in supergravity. As quantitative confirmation of this correspondence, we note that the Kaluza-Klein modes of Type IIB supergravity on $AdS_5\times {\bf S}^5$ match with the chiral operators of ${\cal N}=4$ super Yang-Mills theory in four dimensions. With some further assumptions, one can deduce a Hamiltonian version of the correspondence and show that the ${\cal N}=4$ theory has a large $N$ phase transition related to the thermodynamics of $AdS$ black holes.

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14,084 citations

Journal Article•DOI•

Gauge Theory Correlators from Non-Critical String Theory

[...]

Steven S. Gubser¹, Igor R. Klebanov¹, Alexander M. Polyakov¹•Institutions (1)

Princeton University¹

28 May 1998-Physics Letters B

TL;DR: In this paper, a boundary of the anti-deSitter space analogous to a cut-off on the Liouville coordinate of the two-dimensional string theory is introduced to obtain certain Green's functions in 3+1-dimensional N = 4 supersymmetric Yang-Mills theory with a large number of colors via non-critical string theory.

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11,887 citations

Additional excerpts

...For the SU(N) Yang-Mills theory they are expected to carry the ‘t Hooft factor [3], N, where χ is the Euler character....
[...]

Posted Content•

Anti de sitter space and holography

[...]

Edward Witten

20 Feb 1998-arXiv: High Energy Physics - Theory

TL;DR: In this article, a correspondence between conformal field theory observables and those of supergravity was proposed, where correlation functions in conformal fields are given by the dependence of the supergravity action on the asymptotic behavior at infinity.

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Abstract: Recently, it has been proposed by Maldacena that large $N$ limits of certain conformal field theories in $d$ dimensions can be described in terms of supergravity (and string theory) on the product of $d+1$-dimensional $AdS$ space with a compact manifold. Here we elaborate on this idea and propose a precise correspondence between conformal field theory observables and those of supergravity: correlation functions in conformal field theory are given by the dependence of the supergravity action on the asymptotic behavior at infinity. In particular, dimensions of operators in conformal field theory are given by masses of particles in supergravity. As quantitative confirmation of this correspondence, we note that the Kaluza-Klein modes of Type IIB supergravity on $AdS_5\times {\bf S}^5$ match with the chiral operators of $\N=4$ super Yang-Mills theory in four dimensions. With some further assumptions, one can deduce a Hamiltonian version of the correspondence and show that the $\N=4$ theory has a large $N$ phase transition related to the thermodynamics of $AdS$ black holes.

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8,751 citations

Cites background from "A planar diagram theory for strong ..."

...In large N QCD, such behavior cannot prevail at all temperatures....
[...]
...It is surprising that this comparison will work, since QCD is confining, while the N = 4 theory has no obviously analogous phenomenon....
[...]
...The whole idea of the 1/N expansion as an approach to QCD [1] is that for large N , the Hilbert space of the theory consists of color singlet particles whose masses and...
[...]
...The whole idea of the 1/N expansion as an approach to QCD [1] is that for large N , the Hilbert space of the theory consists of color singlet particles whose masses and multiplicities are independent of N ....
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...We will therefore compare to the expected large N thermodynamics [57] of an SU(N) gauge theory with massive quarks in the fundamental representation (that is, ordinary QCD generalized to large N)....
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Journal Article•DOI•

Large N Field Theories, String Theory and Gravity

[...]

Ofer Aharony¹, Steven S. Gubser², Juan Maldacena², Hirosi Ooguri³, Hirosi Ooguri⁴, Yaron Oz⁵ - Show less +2 more•Institutions (5)

Rutgers University¹, Harvard University², University of California, Berkeley³, Lawrence Berkeley National Laboratory⁴, CERN⁵

01 Jan 2000-Physics Reports

TL;DR: In this paper, the holographic correspondence between field theories and string/M theory is discussed, focusing on the relation between compactifications of string theory on anti-de Sitter spaces and conformal field theories.

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5,610 citations

Cites background from "A planar diagram theory for strong ..."

...The most direct indication from the gauge theory that it could be described in terms of a string theory comes from the ’t Hooft large N limit [3], which we will now describe in detail....
[...]
...It was suggested by ’t Hooft that the theory might simplify when the number of colors N is large [3]....
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...Since ’t Hooft’s work [3] we knew that the large N limit of gauge theories should be described by strings, if the parameter g(2) YMN is kept fixed....
[...]

Journal Article•DOI•

Anti-de Sitter Space, Thermal Phase Transition, And Confinement in Gauge Theories

[...]

Edward Witten¹•Institutions (1)

Princeton University¹

16 Mar 1998-Advances in Theoretical and Mathematical Physics

TL;DR: The correspondence between supergravity and string theory on AdS space and boundary conformal eld theory relates the thermodynamics of N = 4 super Yang-Mills theory in four dimensions to the thermodynamic properties of Schwarzschild black holes in Anti-de Sitter space as mentioned in this paper.

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Abstract: The correspondence between supergravity (and string theory) on AdS space and boundary conformal eld theory relates the thermodynamics of N = 4 super Yang-Mills theory in four dimensions to the thermodynamics of Schwarzschild black holes in Anti-de Sitter space. In this description, quantum phenomena such as the spontaneous breaking of the center of the gauge group, magnetic connement, and the mass gap are coded in classical geometry. The correspondence makes it manifest that the entropy of a very large AdS Schwarzschild black hole must scale \holographically" with the volume of its horizon. By similar methods, one can also make a speculative proposal for the description of large N gauge theories in four dimensions without supersymmetry.

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4,209 citations

Cites background from "A planar diagram theory for strong ..."

...Thus the old prophecy [1] comes to pass: nonperturbative effects close up the holes in the Feynman diagrams, giving a confining theory with a mass gap, and with 1/N as a coupling constant, at least for large η....
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...The dominant string diagrams for large N with fixed g 5N and fixed T are the planar diagrams of ’t Hooft [1] – diagrams of genus zero with any number of holes....
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...Understanding the large N behavior of gauge theories in four dimensions is a classic and important problem [1]....
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...9) is of order 1/N , as expected [1] for the residual interactions between color singlet states in the large N limit....
[...]

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References

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Journal Article•DOI•

Ultraviolet Behavior of Non-Abelian Gauge Theories

[...]

David J. Gross¹, Frank Wilczek¹•Institutions (1)

Princeton University¹

25 Jun 1973-Physical Review Letters

TL;DR: In this paper, it was shown that a wide class of non-Abelian gauge theories have, up to calculable logarithmic corrections, free-field-theory asymptotic behavior.

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Abstract: It is shown that a wide class of non-Abelian gauge theories have, up to calculable logarithmic corrections, free-field-theory asymptotic behavior. It is suggested that Bjorken scaling may be obtained from strong-interaction dynamics based on non-Abelian gauge symmetry.

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3,334 citations

Journal Article•DOI•

Reliable Perturbative Results for Strong Interactions

[...]

H. David Politzer¹•Institutions (1)

Harvard University¹

25 Jun 1973-Physical Review Letters

TL;DR: In this article, the authors show that perturbation theory is arbitrarily good for the deep Euclidean Green's functions of any Yang-Mills theory and of many Yang Mills theories with fermions.

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Abstract: An explicit calculation shows perturbation theory to be arbitrarily good for the deep Euclidean Green's functions of any Yang-Mills theory and of many Yang-Mills theories with fermions. Under the hypothesis that spontaneous symmetry breakdown is of dynamical origin, these symmetric Green's functions are the asymptotic forms of the physically significant spontaneously broken solution, whose coupling could be strong.

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2,826 citations

Journal Article•DOI•

Dimensional regularization and the renormalization group

[...]

Gerard 't Hooft¹•Institutions (1)

CERN¹

24 Sep 1973-Nuclear Physics

TL;DR: In this article, the behavior of a renormalized field theory under scale transformations x → λx; p → p/λ can be found in a simple way when the theory is regularized by the continuous dimension method.

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1,104 citations

Journal Article•DOI•

Three Triplet Model with Double SU(3) Symmetry

[...]

M. Y. Han¹, Yoichiro Nambu²•Institutions (2)

Syracuse University¹, University of Chicago²

21 Apr 1965-Physical Review

TL;DR: In this paper, a model for low-lying baryons and mesons based on three triplets with integral charges is proposed, somewhat similar to the two-triplet model introduced earlier by one of us (Y. N.).

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Abstract: With a view to avoiding some of the kinematical and dynamical difficulties involved in the single-triplet quark model, a model for the low-lying baryons and mesons based on three triplets with integral charges is proposed, somewhat similar to the two-triplet model introduced earlier by one of us (Y. N.). It is shown that in a $U(3)$ scheme of triplets with integral charges, one is naturally led to three triplets located symmetrically about the origin of ${I}_{3}\ensuremath{-}Y$ diagram under the constraint that the Nishijima-Gell-Mann relation remains intact. A double $\mathrm{SU}(3)$ symmetry scheme is proposed in which the large mass splittings between different representations are ascribed to one of the $\mathrm{SU}(3)$, while the other $\mathrm{SU}(3)$ is the usual one for the mass splittings within a representation of the first $\mathrm{SU}(3)$.

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529 citations

Journal Article•DOI•

An algorithm for the poles at dimension four in the dimensional regularization procedure

[...]

Gerard 't Hooft¹•Institutions (1)

CERN¹

08 Oct 1973-Nuclear Physics

TL;DR: In this paper, a simple algorithm is derived to express Δ L in terms of the components of the Lagrangian L without performing integrations, which can be used in dimensional regularization, but also to derive Callan-Symanzik type equations for small distance behaviour in any renormalizable theory.

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399 citations