Quark confinement
Notes on strongly coupled QCD in the continuum
By continuum here we mean using methods different from lattice QCD, which is currently our main instrument for quantitative understanding of QCD physics at strong coupling.
What can we actually do apart from lattice simulations to study properties of QCD in this regime? Not much really. As recent minireview paper by M. Pennington explains, one approach to the problem would be solving Schwinger-Dyson equations at strong coupling.
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Correlator of Wilson and t’Hooft loops at strong coupling in N=4 SYM theory
Andrew Zayakin works at LMU, Munich and ITEP, Moscow. His interests include non-perturbative physics of QCD, string theory and AdS/CFT correspondence. Dmitry.
This post is about my recent paper with Alexander Gorsky and Alexander Monin about a correlator of a Wilson and a ‘t Hooft loop. Before I proceed, I should explain what these objects are and why they are important to be studied. QCD possesses a consistent description in terms of “dual variables” – charges and monopoles. Reader familiar with the systematics of particle-like solutions in different theories would stop me at this very moment by pointing out there are no monopoles in QCD. True, there are no monopoles in the sense of e.g. Georgi-Glashow model. However, effectively there is such a thing as monopole, which is widely observed on lattice as a non-zero Abelian flux through a closed lattice surface. A lot is known on “thermodynamics” and “phenomenology” of these quasiparticles. They do not exist in the sense of theory spectrum. Still, they are an important tool of describing QCD. The QCD phase transition, which is an element of common lore, can easily be understood in terms of monopoles (Fig.1).
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274. Video of the day: Quark-gluon plasma at RHIC
Beautiful promo video of RHIC. Not sure what she means by “they expected to find a gas…” 
226. Top ten open problems in physics
What is the ultimate purpose of my work as theoretical physicist and, if you want, my existence itself? Is it serving the community of other physicists like organizing and participating in conferences? Nop. Then, maybe teaching future physicists in the University, encourage young people to enter the exciting field of physics? Not quite. Writing good papers? Ei. Maybe blogging? Sorry but nein. I think… the ultimate purpose of my work is solving unsolved mysteries in physics. I am afraid, this and only this makes my work enjoyable for me, makes it fun. For the sake of future reference, let me enlist here the most important (from my point of view), hard and interesting unsolved problems in physics.
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172. Color glass condensate and glasma
I am currently reading a paper that, I should admit, I absolutely fell in love with – the one by Larry McLerran called “A brief introduction to the color glass condensate“. What is the reason for me to show up warm feelings? This is because the concentration of non-trivial physical ideas per page is so enormously high in the paper, because the emphasis is on physics and physical ideas rather than on formalities or model building, and because Larry typically just shows you the tail of the idea hiding its body in references – this keeps my mind always focused (clearly, I don’t want to go through tones of references to understand what physics is about )
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170. Back to AdS/QCD – interview with Josh
As you may remember, recently Josh Erlich has made a guest blog post about AdS/QCD at NEQNET. I think that the discussion we had after the post is so terrific that it is worth reposting here in the form of brief interview with Josh. Another reason for reposting is that you, guys, did not want to get into nice physics discussion with Josh, while he was still around (he is attending some conf in Argentina now, as I understand). So, here you go (D. – me, J. – Josh Erlich):
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163. What is AdS/QCD?
This is a a guest post by Josh Erlich from the College of William and Mary, Williamsburg. Dmitry.
This is a summary of AdS/QCD based on a recent review talk I gave at the Confinement 8 conference in Mainz, Germany. For more details and a list of references, the talk is posted on the arxiv as arxiv:0812.4976.
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155. Witten explains how to quantize gauge theory
Long time (almost 6 months?) ago Peter Woit wrote about Yau Birthday Conference and briefly mentioned the talk Edward Witten gave there. I was wondering is there preprint going to appear some day with outline of this talk, and it has finally appeared yesterday in ArXiv.
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140. First two weeks of December at NEQNET
Dear friends
Before I proceed to the (becoming usual already) list of posts published at NEQNET during the last two weeks, let me say a couple of words about the blog itself, which is currently the source of my pride 
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128. Melancholy
Jim Kotsybar has just sent me his another poem, which I liked very much (as usual) and would want to share it with you. And yes, very often such a poem would reflect perfectly the mood of a physicist…
126. From quarks to strings. Migdal-Makeenko equation and AdS-CFT correspondence
Although Lubos wants to see my answer to the poll , I decided to finish my analysis of the recent Polyakov’s paper today.
Page 6. In order to justify my picture I have used intuition coming from the loop equation, while Klebanov and Maldacena appealed to the D brane picture of the gauge fielauds. Both points of view are useful but neither of them lead to the quantitative derivation of gauge/string duality.
Comment. He is talking about the Migdal-Makeenko loop equation for the expectation value of the Wilson loop 
. After Migdal’s groundbreaking proof of the fact that this equation describes a free motion of the contour 
in the large 
limit (1981, if I am not wrong (?), even before the Polyakov’s action), not much progress has been reported in this direction. The main reason is that the Migdal-Makeenko equations are formulated on the lattice, and no their continuum limit is known (it is not clear how to perform the renormalization procedure for loops).
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125. From quarks to strings. On Liouville mode, instantons and confinement in abelian theories
Alexander Polyakov have released this week a preprint about history of string theory, which is also so full of non-trivial physical ideas that I decided to list some of them in this post as well as to include my comments (or rather my ramblings )
122. Where are quarks in the Wilson loop?
An anonymous reader from Spain asks in comments to my “Wilson loop – physical introduction” post:
Why do you interpret a mathematical expresion that displays a gluon field (Amu) as a qqbar loop? Where are the q fields? Why they don’t appear in the Wilson loop but you still interpret they’re there? And where did the gluon go?
I think, these questions are such that the answer to them deserves a separate post, so thanks a lot for asking!
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119. Fun with energy gap for QCD Born-Oppenheimer Hamiltonian
Let us try to solve the Exercise 2 in this post about the Wilson loop. Since we, scientists, are all lazy (as you are!), that’s what I would like to do: I will give three different solutions of the exercise with three different answers Then, if you are interested to learn the subject (and you probably are, becase the subject is quark confinement, right?), you can choose a solution you like most (I will even introduce a poll ) and kindly explain in comments why do you think that two other solutions are wrong The goal of the experiment is to show how applicable is the democracy approach (as advocated by Lee Smolin ) to science.
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118. Last two weeks of November on NEQNET
Well, those two weeks were quite productive ones! – 19 posts in overall (or 20 including this one ) This counts to 1.5 posts per day (and you should take into account that I was on leave to Munich for 4 days). I hope my writing was not too boring for you
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