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one distinguishes bottom-up model building … from bottom-up model building
The former should be ’top-down’?
David, thanks for fixing, I see this only now.
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The extreme form of bottom-up holographic model building is explored in
where an appropriate bulk geometry is computer-generated from specified boundary behaviour.
started a further subsection on Type0/YM correspondence:
Instead of starting with M5-branes in locally supersymmetric M-theory and then spontaneously breaking all supersymmetry by suitable KK-compactification as in the Witten-Sakai-Sugimoto model, one may start with a non-supersymmetric bulk string theory in the first place.
In this vein, it has been argued in GLMR 00 that there is holographic duality between type 0 string theory and non-supersymmetric 4d Yang-Mills theory (hence potentially something close to QCD).
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Added pointer to more of the original references on modelling baryons by wrapped branes:
{#BISY98} A. Brandhuber, N. Itzhaki, J. Sonnenschein, S. Yankielowicz Baryons from Supergravity, JHEP 9807:020,1998 (arxiv:hep-th/9806158)
Yosuke Imamura, Baryon Mass and Phase Transitions in Large N Gauge Theory, Prog. Theor. Phys. 100 (1998) 1263-1272 (arxiv:hep-th/9806162)
Yosuke Imamura, Supersymmetries and BPS Configurations on Anti-de Sitter Space, Nucl. Phys. B537:184-202,1999 (arxiv:hep-th/9807179)
{#CGS98} Curtis G. Callan, Alberto Guijosa, Konstantin G. Savvidy, Baryons and String Creation from the Fivebrane Worldvolume Action (arxiv:hep-th/9810092)
Curtis G. Callan, Alberto Guijosa, Konstantin G. Savvidy, Oyvind Tafjord, Baryons and Flux Tubes in Confining Gauge Theories from Brane Actions, Nucl. Phys. B555 (1999) 183-200 (arxiv:hep-th/9902197)
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Understanding the nucleon structure is one of the most important research topics in fundamental science, and tremendous efforts have been done to deepen our knowledge over several decades. $[...]$ Since $[these]$ are highly nonperturbative physical quantities, in principle they are not calculable by the direct use of QCD. Furthermore, although there is available data, this has large errors. These facts cause the huge uncertainties which can be seen in the preceding studies based on the global QCD analysis.
In this work, we investigate the gluon distribution at small x by calculating the DIS structure functions in the framework of holographic QCD, which is constructed based on the AdS/CFT correspondence.
I have added a slightly improved diagram of the brane configurations (here), now also including the “monopole D6-branes”, and including a second diagram that shows them from another point of view.
Will be using this now to add some content at D6-D8 brane intersection
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am adding references on perturbative string theory-corrections (for small ’t Hooft coupling $\lambda = g_{YM}^2 N$) and/or M-theory-corrections (for small N) to the supergravity-approximation of the AdS/CFT correspondence:
There is this one on the general need for M-theory at small $N_c$ in gauge/gravity duality:
and this one more specifically for AdS/QCD:
Hopefully there is more…
one more reference on stringy corrections:
one more:
B. Basso, Cusp anomalous dimension in planar maximally supersymmetric Yang-Mills theory (spire:858223)
“The result $[$(29)$]$ coincides exactly with the recent two-loop stringy correction computed in Alday-Maldacena 07, providing a striking confirmation of the AdS/CFT correspondence.”
But I should rather start an entry large 1/N limit and assemble references there
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Piljin Yi, Holographic Baryons (arXiv:0902.4515, doi:10.1142/9789814280709_0016), Chapter 16 in: Mannque Rho, Ismail Zahed (eds.) The Multifaceted Skyrmion, World Scientific 2016 (doi:10.1142/9710)
Piljin Yi, Precision Holographic Baryons, AIP Conference Proceedings 1388, 106 (2011) (arXiv:1103.1684, doi:10.1063/1.3647358)
Piljin Yi, Two Approaches to Holographic Baryons/Nuclei, Few-Body Syst (2013) 54: 77. (doi:10.1007/s00601-012-0373-7)
added a long quote from Yi 09:
QCD is a challenging theory. Its most interesting aspects, namely the confinement of color and the chiral symmetry breaking, have defied all analytical approaches. While there are now many data accumulated from the lattice gauge theory, the methodology falls well short of giving us insights on how one may understand these phenomena analytically, nor does it give us a systematic way of obtaining a low energy theory of QCD below the confinement scale.
$[...]$
it has been proposed early on that baryons are topological solitons, namely Skyrmions $[$ but $]$ the usual Skyrmion picture of the baryon has to be modified significantly in the context of full QCD. $[...]$ the holographic picture naturally brings a gauge principle in the bulk description of the flavor dynamics in such a way that all spin one mesons as well as pions would enter the $[$ skyrmionic-$]$construction of baryons on the equal footing.
$[...]$
holographic QCD is similar to the chiral perturbation theory in the sense that we deal with exclusively gauge-invariant operators of the theory. The huge difference is, however, that this new approach tends to treat all gauge-invariant objects together. Not only the light meson fields like pions but also heavy vector mesons and baryons appear together, at least in principle. In other words, a holographic QCD deals with all color-singlets simultaneously, giving us a lot more predictive power.
$[...]$
The expectation that there exists a more intelligent theory consisting only of gauge-invariant objects in the large Nc limit is thus realized via string theory in a somewhat surprising manner that the master fields, those truly physical degrees of freedom, actually live not in four dimensional Minkowskian world but in five or higher dimensional curved geometry. This is not however completely unanticipated, and was heralded in the celebrated work by Eguchi and Kawai in early 1980’s which is all the more remarkable in retrospect.
$[...]$
To compare against actual QCD, we must fix $[$ the ’t Hooft coupling and the KK-scale $]$ to fit both the pion decay constant $f_\pi$ and the mass of the first vector meson. After this fitting, all other infinite number of masses and coupling constants are fixed. This version $[$ the WSS model $]$of the holographic QCD is extremely predictive.
$[...]$
$[$this $]$ elevates the classic Skyrme picture based on pions to a unified model involving all spin one mesons in addition to pions. This is why the picture is extremely predictive.
As we saw in this note, for low momentum processes, such as soft pion processes, soft rho meson exchanges, and soft elastic scattering of photons, the $[$ WSS-$]$model’s predictions compare extremely well with experimental data. It is somewhat mysterious that the baryon sector works out almost as well as the meson sector
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One can make $[$chiral perturbation theory$]$ consistent with QCD by suitably matching the correlators of the effective theory to those of QCD at a scale near $\Lambda$. Clearly this procedure is not limited to only one set of vector mesons; in fact, one can readily generalize it to an infinite number of hidden gauge fields in an effective Lagrangian. In so doing, it turns out that a fifth dimension is “deconstructed” in a (4+1)-dimensional (or 5D) Yang–Mills type form. We will see in Part III that such a structure arises, top-down, in string theory.
$[...]$
$[$this holographic QCD$]$ model comes out to describe — unexpectedly well — low-energy properties of both mesons and baryons, in particular those properties reliably described in quenched lattice QCD simulations.
$[...]$
One of the most noticeable results of this holographic model is the first derivation of vector dominance (VD) that holds both for mesons and for baryons. It has been somewhat of an oddity and a puzzle that Sakurai’s vector dominance — with the lowest vector mesons ρ and ω — which held very well for pionic form factors at low momentum transfers famously failed for nucleon form factors. In this holographic model, the VD comes out automatically for both the pion and the nucleon provided that the infinite $[$KK-$]$tower is included. While the VD for the pion with the infinite tower is not surprising given the successful Sakurai VD, that the VD holds also for the nucleons is highly nontrivial. $[...]$ It turns out to be a consequence of a holographic Cheshire Cat phenomenon
Am compiling a reply to Orland 20/03/10 11:11.
Here is what I might say, if I am allowed to say it there:
That the quark model correctly predicts hadron bound states is a purely computer-experimental observation (established only fairly recently for the first few hadrons arXiv:0906.3599) of which a conceptual understanding remains an open problem, dubbed one of the Millennium Problems.
While it is an old idea that the string model of mesons gives a conceptual handle on the confinement mechanism, its detailed and quantitatively accurate development used to be lacking. Making the string model of hadrons actually work is what holographic QCD is all about.
Since holographic QCD readily explains fundamental characteristics of confined QCD that remain mysterious not just in the quark model but also in popular ad hoc strong coupling model building such as the bag model (not only the confinement and chiral symmetry breaking mechanism itself, but also for instance vector meson dominance and the Cheshire cat property of the bag model are readily explained by holographic QCD) it is attractive to researchers interested in real-world QCD (e.g. Rho et al. 16, doi:10.1142/9710).
The Skyrme model for hadrons is in fact reasonable not in its original form but only after adjoining the tower of vector mesons to the pion. But in that tower-corrected form the Skyrme model works wonders: nuclei all the way up to carbon(!) are well-decribed already by Skyrmions in the pion+rho field (arXiv:1811.02064). This tower-correction of the old Skyrmion model had let nuclear physicist to discover (PhysRevD.69.065020) the hidden 5th dimension, leading to proof of vector meson dominance for nucleons. Conversely, the tower-corrected Skrymion model emerges from holographic QCD, where all mesons are unified as the transversal KK-modes of the 5d flavour gauge theory.
That available results in holographic AdS/QCD currently only (“only”) address the strongly coupled confined QCD phase and not its asymptotically free UV is not intrinsic to the holographic theory but owed to its computational development: holography is studied for strong ’t Hooft coupling only for the convenience to be able to disregard string-scale and strong string-coupling effects on the bulk side. Inclusion of small-N corrections into AdS/QCD to get the full picture remains to be developed but need not and is not being ignored (e.g. PhysRevD.74.076004).
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Hence from the perspective of small-N corrected holographic QCD, the mass gap problem/confinement problem translates to the problem of formulating M-theory
Is the mass gap problem a feasible target for you, then?
We are currently writing up a derivation, from Hypothesis H, of at least parts of quantum hadrodynamics. Wanted to have something out already a while ago, but getting bogged down in a zoo of details.
This is different from but much in the spirit of the derivation of hadrodynamics via AdS/QCD, which really comes down to the observation that string phenomenology all falls into place when working on flavor branes instead of color branes. (Notably, both supersymmetry and the KK-tower are observed, and have been for decades, in the hadron spectrum – that’s the statement of hadron supersymmetry and of the derivation of the vector-meson-corrected Skyrme model from KK-reduction of 5d Yang-Mills (here)).
In these stringy derivations of hadrodynamics, the traditional logic is reversed: Instead of first being handed chromodynamics by the gods, with the task to prove/exhibit the mass gap/confinement-transition to the hadronic phase, one instead finds hadrodynamics from first principles, without transitioning through, or even mentioning, chromodynamics.
I am wondering if one should really ask the “reverse mass gap problem”: Given “the” massive theory of quantum hadrodynamics, show that asymptotically free chromodynamics emerges as an appropriate limiting case.
More generally, I am wondering if the focus on color physics has been misleading mankind in a grandiose way: Notice how the LHC keeps spitting out more and more new particles, for instance the increasing number of XYZ particles, while at the same time some people complain that nothing new is being seen. The reason for this stark contrast is of course the tacit assumption that chromodynamics implies all hadron physics, by which logic any new hadron being observed is “just a resonance”.While this is the common lore dominating all popular exposition, it is actually a huge leap of faith. In reality, very little hadron physics is really explained by the standard model of particle physics! People point here to lattice QCD computations for “steady progress”, but not only is applicability of lattice QCD more restricted than often acknowledged, but in fact each and every lattice QCD computation needs chiral perturbation theory (hence models of hadrodynamics!) for translating its results to “physical quark masses”. That’s fine for phenomenology, but is circular as a claim of a first-principles derivation of hadrodynamics from QCD.
I want to write a pamphlete: Against Color. But need to get other things out of the way first.
Fascinating, thanks!
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remarkable
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added pointer to the tandem talks on string-realization of QCD, at the Strings2021 meeting yesterday
Igor Klebanov, Remarks on Color Confinement, talk at Strings 2021 (pdf, video)
Sergei Dubovsky, Comments on (mostly long) QCD strings, talk at Strings 2021 (pdf, video)
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For what it’s worth, today this nLab entry is referenced by Quanta Magazine (or “hover-linked”, at least ;-)
see here
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Am adding this also at anomalous magnetic moment.
added (here) a further table of predictions/fits of hadron masses, now incorporating also the first heavy quark contibutions (from totay’s Chen & Huang 2021)
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P. 3:
The derived parameters are shown to corroborate experimental data with great accuracy
towards the beginning of the Idea-section I added one sentence (here) briefly highlighting that QCD is not as such conformally invariant – but then added a pointer to today’s
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(kudos to the authors for citing the nLab: p. 2 :-)
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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. More over, 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.
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together with a screenshot of their table of predicted versus measured meson masses
added pointer to further original articles by Polyakov
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]
and to this historical review
But I think I will now copy all these Polyakov-references into an !include
-file
Polyakov gauge-string duality – references
and then re-include them here and in related entries
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40:13: “Personally, I think this setup really implies that pure $SU(N)$ gauge theory is dual to a string theory.
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