general mechanisms
electric-magnetic duality, Montonen-Olive duality, geometric Langlands duality
string-fivebrane duality
string-QFT duality
QFT-QFT duality:
effective QFT incarnations of open/closed string duality,
relating (super-)gravity to (super-)Yang-Mills theory:
Seiberg duality (swapping NS5-branes)
algebraic quantum field theory (perturbative, on curved spacetimes, homotopical)
quantum mechanical system, quantum probability
interacting field quantization
The semiclassical approximation to bottom-up holographic QCD is light front holographic QCD, named after the light cone-coordinates in terms if which the effective Schrödinger equation for the quarks is written.
Background on light-front QCD for quantum hadrodynamics:
International Light Cone Advisory Committee, Light-Front Quantum Chromodynamics: A framework for the analysis of hadron physics, Nuclear Physics B - Proceedings Supplements Volumes 251–252, June–July 2014, Pages 165-174 (arXiv:1309.6333, doi:10.1016/j.nuclphysbps.2014.05.004)
Edward Shuryak, Ismail Zahed, Hadronic structure on the light-front I: Instanton effects and quark-antiquark effective potentials (arXiv:2110.15927)
Edward Shuryak, Ismail Zahed, Hadronic structure on the light-front II: QCD strings, Wilson lines and potentials (arXiv:2111.01775)
Original articles on holographic LFQCD:
Stanley Brodsky, Guy de Teramond, Light-Front Hadron Dynamics and AdS/CFT Correspondence, Phys. Lett. B 582 (2004) 211-221 [arXiv:hep-th/0310227, doi:10.1016/j.physletb.2003.12.050]
Guy de Teramond, Stanley Brodsky, Light-Front Holography: A First Approximation to QCD, Phys. Rev. Lett. 102 (2009) 081601 [doi:10.1103/PhysRevLett.102.081601, arXiv:0809.4899]
Relation to renormalization (field-strength renormalization):
Review:
Stanley Brodsky, Guy de Teramond, Hans Günter Dosch, Joshua Erlich, Light-Front Holographic QCD and Emerging Confinement, Physics Reports Volume 584, 8 July 2015, Pages 1-105 (arXiv:1407.8131)
Alexandre Deur, Stanley Brodsky, Guy de Teramond, Section 4.2 of: The QCD Running Coupling, Prog. Part. Nuc. Phys. 90 1 (2016) (arXiv:1604.08082, doi:10.1016/j.ppnp.2016.04.003)
Liping Zou, Hans Günter Dosch, A very Practical Guide to Light Front Holographic QCD, (arXiv:1801.00607)
Stanley Brodsky, Color Confinement and Supersymmetric Properties of Hadron Physics from Light-Front Holography, International Conference on Beauty, Charm and Hyperon Hadrons (BEACH 2018) 17–23 June 2018, Peniche, Portugal (arXiv:1912.12578)
Ruben Sandapen, An overview of light-front holography (arXiv:2001.03479)
Stanley Brodsky, Guy de Teramond, Hans Günter Dosch, Light-Front Holography and Supersymmetric Conformal Algebra: A Novel Approach to Hadron Spectroscopy, Structure, and Dynamics (arXiv:2004.07756)
Stanley Brodsky, Supersymmetric and Other Novel Features of Hadron Physics from Light-Front Holography, Proceedings of the 24th Workshop, “What Comes Beyond the Standard Models” (arXiv:2112.02453)
Guy de Téramond, Emergent phenomena in QCD: The holographic perspective [arXiv:2212.14028]
Further concerning confinement and chiral symmetry breaking:
Specifically regarding rho-mesons:
See also
Harun Omer, Embedding LFHQCD in Worldsheet String Theory (arXiv:1909.12866)
Alfredo Vega, Miguel Angel Martin Contreras, Two-body light front wave functions from general AdS/QCD models (arXiv:2005.04501)
Dmitriy N. Kim, Gerald A. Miller, Light-Front Holography Model of the EMC Effect [arXiv:2209.13753]
Application to B-meson physics:
Discussion of hadron supersymmetry via light cone supersymmetric quantum mechanics in holographic light front QCD:
Guy de Teramond, Hans Günter Dosch, Stanley Brodsky, Baryon Spectrum from Superconformal Quantum Mechanics and its Light-Front Holographic Embedding, Phys. Rev. D 91, 045040 (2015) (arXiv:1411.5243)
Hans Günter Dosch, Guy de Teramond, Stanley Brodsky, Supersymmetry Across the Light and Heavy-Light Hadronic Spectrum, Phys. Rev. D 92, 074010 (2015) (arXiv:1504.05112)
Stanley Brodsky, Guy de Téramond, Hans Günter Dosch, Cédric Lorcé, Meson/Baryon/Tetraquark Supersymmetry from Superconformal Algebra and Light-Front Holography, International Journal of Modern Physics AVol. 31, No. 19, 1630029 (2016) (arXiv:1606.04638)
Hans Günter Dosch, Guy de Teramond, Stanley Brodsky, Supersymmetry Across the Light and Heavy-Light Hadronic Spectrum II, Phys. Rev. D 95, 034016 (2017) (arXiv:1612.02370)
Marina Nielsen, Stanley Brodsky, Hadronic Superpartners from Superconformal and Supersymmetric Algebra, Phys. Rev. D 97, 114001 (2018) (arXiv:1802.09652)
Marina Nielsen, Stanley Brodsky, Guy F. de Téramond, Hans Günter Dosch, Fernando S. Navarra, Liping Zou, Supersymmetry in the Double-Heavy Hadronic Spectrum, Phys. Rev. D 98, 034002 (2018) (arXiv:1805.11567)
In view of tetraquarks:
Key ideas underlying what is now known as holographic duality in string theory and specifically as holographic QCD (see notably also at holographic light front QCD) were preconceived by Alexander Polyakov (cf. historical remarks in Polyakov (2008)) under the name gauge/string duality (cf. historical review in Polyakov (2008)), in efforts to understand confined QCD (the mass gap problem) by regarding color-flux tubes (Wilson lines) between quarks as dynamical strings:
Early suggestion that confined QCD is described by regarding the color-flux tubes as string-like dynamical degrees of freedoms:
John Kogut, Leonard Susskind, Vacuum polarization and the absence of free quarks in four dimensions, Phys. Rev. D 9 (1974) 3501-3512 $[$doi:10.1103/PhysRevD.9.3501$]$
Kenneth G. Wilson, Confinement of quarks, Phys. Rev. D 10 (1974) 2445 $[$doi:10.1103/PhysRevD.10.2445$]$
(argument in lattice gauge theory)
John Kogut, Leonard Susskind, Hamiltonian formulation of Wilson’s lattice gauge theories, Phys. Rev. D 11 (1975) 395 $[$doi:10.1103/PhysRevD.11.395$]$
“The gauge-invariant configuration space consists of a collection of strings with quarks at their ends. The strings are lines of non-Abelian electric flux. In the strong coupling limit the dynamics is best described in terms of these strings. Quark confinement is a result of the inability to break a string without producing a pair. $[$…$]$”
“The confining mechanism is the appearance of one dimensional electric flux tubes which must link separated quarks. The appropriate description of the strongly coupled limit consists of a theory of interacting, propagating strings. $[$…$]$”
“This picture of the strongly coupled Yang-Mills theory in terms of a collection of stringlike flux lines is the central result of our analysis. It should be compared with the phenomenological use of stringlike degrees of freedom which has been widely used in describing hadrons.”
Alexander Polyakov, String representations and hidden symmetries for gauge fields, Physics Letters B 82 2 (1979) 247-250 $[$doi:10.1016/0370-2693(79)90747-0$]$
Alexander Polyakov, Gauge fields as rings of glue, Nuclear Physics B 164 (1980) 171-188 $[$doi:10.1016/0550-3213(80)90507-6$]$
“The basic idea is that gauge fields can be considered as chiral fields, defined on the space of all possible contours (the loop space). The origin of the idea lies in the expectation that, in the confining phase of a gauge theory, closed strings should play the role of elementary excitations.”
Yuri Makeenko, Alexander A. Migdal, Quantum chromodynamics as dynamics of loops, Nuclear Physics B 188 2 (1981) 269-316 $[$doi:10.1016/0550-3213(81)90258-3$]$
“So the world sheet of string should be interpreted as the color magnetic dipole sheet. The string itself should be interpreted as the electric flux tube in the monopole plasma.”
Alexander Polyakov, Gauge Fields and Strings, Routledge, Taylor and Francis (1987, 2021) $[$doi:10.1201/9780203755082, oapen:20.500.12657/50871$]$
$[$old personal page$]$: “My main interests this year $[$1993?$]$ were directed towards string theory of quark confinement. The problem is to find the string Lagrangian for the Faraday’s ”lines of force“,which would reproduce perturbative corrections from the Yang-Mills theory to the Coulomb law at small distances and would give permanent confinement of quarks at large distances.”
Cf. also
Early suggestion, due to the Liouville field seen in the quantization of the bosonic string via the Polyakov action,
that such flux tubes regarded as confining strings are to be thought of a probing higher dimensional spacetime, exhibiting a holographic principle in which actual spacetime appears as a brane:
Alexander Polyakov, String Theory and Quark Confinement, talk at Strings’97, Nucl. Phys. Proc. Suppl. 68 (1998) 1-8 $[$arXiv:hep-th/9711002, doi:10.1016/S0920-5632(98)00135-2$]$
“In other words the open string flies in the $(x,\phi)$-space keeping its feet (its ends) on the ground $(\phi=0)$.”
Alexander Polyakov, The wall of the cave, Int. J. Mod. Phys. A 14 (1999) 645-658 $[$arXiv:hep-th/9809057, doi:10.1142/S0217751X99000324$]$
“We add new arguments that the Yang-Mills theories must be described by the non-critical strings in the five dimensional curved space. The physical meaning of the fifth dimension is that of the renormalization scale represented by the Liouville field.”
eventually culminating in the formulation of the dictionary for the AdS-CFT correspondence:
“Relations between gauge fields and strings present an old, fascinating and unanswered question. The full answer to this question is of great importance for theoretical physics. It will provide us with a theory of quark confinement by explaining the dynamics of color-electric fluxes.”
and the suggestion of finding the string-QCD correspondence:
“in the strong coupling limit of a lattice gauge theory the elementary excitations are represented by closed strings formed by the color-electric fluxes. In the presence of quarks these strings open up and end on the quarks, thus guaranteeing quark confinement. Moreover, in the $SU(N)$ gauge theory the strings interaction is weak at large $N$. This fact makes it reasonable to expect that also in the physically interesting continuous limit (not accessible by the strong coupling approximation) the best description of the theory should involve the flux lines (strings) and not fields, thus returning us from Maxwell to Faraday. In other words it is natural to expect an exact duality between gauge fields and strings. The challenge is to build a precise theory on the string side of this duality.”
Historical reminiscences:
“Already in 1974, in his famous large $N$ paper, ‘t Hooft already tried to find the string-gauge connections. His idea was that the lines of Feynman’s diagrams become dense in a certain sense and could be described as a 2d surface. This is, however, very different from the picture of strings as flux lines. Interestingly, even now people often don’t distinguish between these approaches. In fact, for the usual amplitudes Feynman’s diagrams don’t become dense and the flux lines picture is an appropriate one. However there are cases in which t’Hooft’s mechanism is really working.”
Alexander M. Polyakov, §1 in: Beyond Space-Time, in The Quantum Structure of Space and Time, Proceedings of the 23rd Solvay Conference on Physics, World Scientific (2007) $[$arXiv:hep-th/0602011, pdf$]$
Alexander M. Polyakov, From Quarks to Strings $[$arXiv:0812.0183$]$
published as Quarks, strings and beyond, section 44 in: Paolo Di Vecchia et al. (ed.), The Birth of String Theory, Cambridge University Press (2012) 544-551 $[$doi:10.1017/CBO9780511977725.048$]$
“By the end of ’77 it was clear to me that I needed a new strategy $[$for understanding confinement$]$ and I became convinced that the way to go was the gauge/string duality. $[$…$]$”
“Classically the string is infinitely thin and has only transverse oscillations. But when I quantized it there was a surprise – an extra, longitudinal mode, which appears due to the quantum ”thickening“ of the string. This new field is called the Liouville mode. $[$…$]$”
“I kept thinking about gauge/strings dualities. Soon after the Liouville mode was discovered it became clear to many people including myself that its natural interpretation is that random surfaces in 4d are described by the strings flying in 5d with the Liouville field playing the role of the fifth dimension. The precise meaning of this statement is that the wave function of the general string state depends on the four center of mass coordinates and also on the fifth, the Liouville one. In the case of minimal models this extra dimension is related to the matrix eigenvalues and the resulting space is flat.”
“Since this 5d space must contain the flat 4d subspace in which the gauge theory resides, the natural ansatz for the metric is just the Friedman universe with a certain warp factor. This factor must be determined from the conditions of conformal symmetry on the world sheet. Its dependence on the Liouville mode must be related to the renormalization group flow. As a result we arrive at a fascinating picture – our 4d world is a projection of a more fundamental 5d string theory. $[$…$]$”
“At this point I was certain that I have found the right language for the gauge/string duality. I attended various conferences, telling people that it is possible to describe gauge theories by solving Einstein-like equations (coming from the conformal symmetry on the world sheet) in five dimensions. The impact of my talks was close to zero. That was not unusual and didn’t bother me much. What really caused me to delay the publication (Polyakov 1998) for a couple of years was my inability to derive the asymptotic freedom from my equations. At this point I should have noticed the paper of Klebanov 1997 in which he related D3 branes described by the supersymmetric Yang Mills theory to the same object described by supergravity. Unfortunately I wrongly thought that the paper is related to matrix theory and I was skeptical about this subject. As a result I have missed this paper which would provide me with a nice special case of my program. This special case was presented little later in full generality by Juan Maldacena (Maldacena 1997) and his work opened the flood gates.”
A detailed monograph:
N. D. Hari Dass, Strings to Strings – Yang-Mills Flux Tubes, QCD Strings and Effective String Theories, Lecture Notes in Physics 1018, Springer (2024) [doi:10.1007/978-3-031-35358-1]
Ch. 23:
Effective String Theories (EST) of Yang-Mills Flux Tubes [doi:10.1007/978-3-031-35358-1_22, arXiv:2312.10629]
Last revised on July 13, 2023 at 20:44:10. See the history of this page for a list of all contributions to it.