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Maldacena's fairy-tale on exchange rates, gauge theories, and the Higgs

Juan Maldacena wrote a popular essay on gauge symmetries and their breaking:

The symmetry and simplicity of the laws of physics and the Higgs boson (PDF).
It's sometimes being said that Einstein's discovery of the special theory of relativity was helped by Einstein's work with the patents dealing with the train synchronization. I think that it's not really true (Einstein was stunned by the apparent contradiction between Maxwell's field theory and Newtonian mechanics long before he worked with the patents: sorry, Peter Galison) but it's good enough as a fairy-tale.

The next Maldacena may arrive from Zimbabwe.

Analogously, we learn that Maldacena's work with gauge theories was helped by the chronic inflation in his homeland, Argentina. The persistent monetary inflation and currency reforms – something that many of us consider to be "once in a century" painful event – became as mundane in Argentina as a gauge transformation. In fact, as Maldacena shows (and he is not the first one, I guess), it is not just an analogy. The switching to another unit of wealth is a special case of a gauge transformation.

With this experience, a European or North American gauge theorist facing Maldacena must feel just like a European soccer player facing Argentina, if we recall another observation by Juan at Strings 2014.

The paper is full of images from Wikipedia. The beginning is all about the Beauty and the Beast and the concept of symmetry. You are also reminded about the electricity and magnetism.

But the financial representation of the gauge field \(A_\mu\) and the gauge symmetry is the most interesting thing, of course. The financial gauge group is isomorphic to \(\RR\) but otherwise it works well. Maldacena offers you a financial interpretation of the field strength \(F_{\mu\nu}\) as well, of course.

If you think about a lattice version of the gauge theory, the links correspond to a "conversion of one currency from another". If you go around a loop constructed from these links, the exchange rates may be mismatched and you may earn (or lose) money. Your original assets ("before" you make the round trip) get pretty much multiplied by a factor\[

{\rm Assets}_{\rm after} = {\rm Assets}_{\rm before} \cdot \exp(\text{Magnetic flux})

\] if I add a formula to Maldacena's presentation. The exponential is the monodromy, the Wilson loop without any trace. You shouldn't forget that the trading gauge group is noncompact.

In the real world, we have to consider all these objects in the quantum mechanical language, as Maldacena discusses in another section, and the too obviously wrong consequences of the most naive realization of the symmetry must be avoided by the spontaneous symmetry breaking, the Higgs mechanism.

If someone likes semi-technical popular texts on physics, I recommend it.

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snail feedback (27) :

reader Sam Malik said...

Thank you
for sharing this great article. Game
Development Tutorials

reader Dilaton said...

Haha this might be cool fun of exactly the kind I like best, I will look at it ... :-)))

reader TomVonk said...

I quite agree with this analysis.
Since the Crimea crisis I have been always saying that Russia's leaders are more pragmatic and intelligent than most Western leaders, A.Merkel being a possible exception because she is not really "western".
Even if Russia can probably not sustainably occupy a large hostile country like Ukraine because we are no more in the 40ies and 50ies where a country could "win" just because it had more tanks, this is not really the point.
The point is that I am sure that Putin&Co knows that Russia actually has no interest to try to occupy a large hostile country because it has much to loose and little to win in the process.
Territory ? Russia is already the largest country in the world and most of it is empty anyway. It doesn't need more space.
Population ? Hostile population is unlikely to magically transform in patriotic Russians. On the contrary .
Ressources ? It is not the little coal in Ukraine that can be motivating for one of the most ressources rich country in the world.
Economy ? Krimea is already a burden on Russian finances and Ukraine would be so even more.
Geostrategical advantage ? While this is true for Krimea it is absolutely not true for the vast ukrainian plains and swamps in the middle of nowhere. OK it would be a good starting basis to invade Czechoslovakia or Romania but I am not sure that Putin would be enthousiastic for such a target :)
So what stays that if a part of the territory is populated by a large russian or pro-russian majority and if it can be annexed with no particular difficulty (actually the biggest effort would be to wield a pen to sign some paper like in Crimea) and the territory would not be a too big drain on Russian finances, then they could do this pen wielding bit. But not more.
Yes, I think that sooner or later and regardless what the clueless western politicians say, there will just be one day a bilateral understanding between Russia and Ukraine (obviously they would invite neither the US nor the EU) that it would be better for everybody if some little, far eastern unruly ukrainian provinces simply joined Russia in some to be defined form.
Up to Putin then to disarm the militias and to restore the Pax Russiana what is something he's quite good at.
Perhaps there would even be a gesture from Russia giving Ukraine a few cents on a long term contract gaz price and everybody would be happy.

reader Claudius_II said...

I think we need to ask Ms. Garver, why the 200 MM$ rocket to supply the space station, launched by NASA, exploded yesterday (10/28/14). I'm sure she could enlighten us.

reader Luboš Motl said...

I agree, Tom. Concerning Donbas' annexation by Russia, I am uncertain whether it is a net positive for Russia, leaning towards Yes. It is or at least was industrial, friendly enough, and the annexation would be good for the Russian voters. But the rest of Ukraine... unlikely.

reader Uncle Al said...

Only the photon universe is symmetric! Parity violations, symmetry breakings, chiral anomalies, baryogenesis, biological homochirality, Chern-Simons repair of Einstein-Hilbert action are consistent with vacuum trace chiral anisotropy toward (fermion quarks, hadronic) matter. Applying photon vacuum symmetries toward matter could be the problem with both quantum gravitation and SUSY empiricalnon-detection.

Noether's theorems couple exact vacuum isotropy with conservation of angular momentum. Vacuum trace chiral anisotropy selective to hadronic matter leaks conservation as MoND's 1.2×10^(-10) m/s^2 Milgrom acceleration. Dark matter non-detection is explained. Let's look at three bench top experiments in existing apparatus,
Comments. "see more" for the graphics.
Might stillbe posted, might be "cleansed."

reader thejollygreenman said...

Hi Lubos,
I do like your analysis of the Ukrainian elections and agree with your conclusions. On a different note. I saw an interview with Putin soon after the Crimea became part of Russia, following the popular vote there. Putin were addressing foreign journalists, and in reply to a question from a French journalist made the following remarks.

If Russia were to take over the whole of the Ukraine it would have to offer all the Ukrainian civil service pensioners, police, firemen, nurses, council workers, etc. Russian pensions, At this moment in time it would mean a three-fold increase in pensions for the Ukrainians, and it would wipe out the foreign exchange holdings of Russia, which took 10 years of hard slog to accumulate. Paying the pensioners in the Crimean Russian pensions would cost the Russian treasury $80 million in this financial year, which they haven't budgeted for, they will have to shift accounts around to make that possible, but they - the Russians - could not accommodate the whole of the Ukraine. Am I the only guy that watched Putin give this answer like a beanie from a prudent Dutch or Belgian insurance company?

reader QsaTheory said...

The math for physics has been used to model many other fields

Random Matrix Theory and Cross-correlations in Global

Financial Indices and Local Stock Market Indices

reader Truth said...

Gauge symmetries are not real. They are only redundancies in the description. So why is he making a big fuss over it?

reader Luboš Motl said...

Multiple currencies to measure the wealth are not "real", either, but people make a big fuss over them, nevertheless.

Gauge symmetries are not "real" but they are unavoidable for a manifestly Lorentz-covariant formulation of theories with spin-1 particles which is why they are very important to be learned about.

Being "real" is something completely different than being "an important concept in physics". The wave function isn't "real", either, but it's essential for all of modern physics.

reader Luboš Motl said...

Very true, he could produce and exploit all these numbers from the practical life at 3 a.m. if you woke him up.

Concerning the broader point, of course that in principle, Ukrainians wouldn't *have* to be treated on par with the Russians. They could become 2nd class citizens with 3 times smaller pensions. But this quote by Putin did indicate that he's not planning anything like that in his country. Which, by the way, might be counterproductive. The country is so large that some non-uniformity in pensions etc. would probably be very desirable.

reader Ross Presser said...

For what it's worth, I was complaining that someone ON THE COMIC FORUM had written "reading is hard". I did not come up with that utterance myself.

reader john said...

Off topic: Dear Lubos, I think following link is relevant for your post about linux some time ago:

Note that I share your feelings and opinions towards "free" things but I think linux is much better than yoy think. The above link offers and explanation.

reader Luboš Motl said...

Dear John, my criticism of the arrangement isn't an ad hominem criticism of the programming quality of the particular people who write this or that. What I criticize is the unaccountable, competition-breaking environment that is inseparable from activities separated from the profit.

reader john said...

No, of course I understand your criticism. By "free things" I meant similar things. However the companies who pay linux programmers have a profit motive. There is competition here and programmers paid by companies has responsibility. They also need to fix bad parts of linux developed by someone else ( I guess).

reader Tavrik said...

I think that there is only one country that wants Ukraine and has the money to pay for it- China. They want the farmland and could probably operate the coal, steel, chemical and other industries at a profit.
But China will refuse to deal with the mafia-like oligarchs and crazy Nazi's. After Ukraine defaults on all its debts and is being run by reasonable people then China will start providing assistance, which the US and EU cannot afford to do.

reader RAF III said...

Lubos - Thanks for posting about this essay of Maldacena's. I don't think I would have seen it otherwise. It reminded me of the sort of popular science writing that was commonplace fifty years ago and is now practically extinct.

reader Luboš Motl said...

I have the same impression, and I find this change in the West's dominant subgenres of popularization in the last 50 years unfortunate.

Juan is not quite living in the Western time - and fads. He's Argentine. It may have the same effect as being Czech – it's simply not a problem if we still find some cultural things that were widespread in the West 50 years ago to be hot.

reader RAF III said...

Lubos - I would be pleasantly surprised to find that certain nations and peoples still valued such things, but fear that the West has become too homogenized for that to be true.
I would put it down to the fact that Maldacena is a first rate physicist.
Physics, as the hardest of sciences, is somewhat more resistant to the 'fads' that have overwhelmed the rest of western culture. And Maldacena, having risen to the top, would be quite familiar with good popular science writing. He also, unlike many popularizers, knows what he's talking about! He understands the limitations of a good explanatory analogy and stays within them. He is not concerned with entertaining or reassuring his readers about life, the universe and everything, but actually makes demands of them. Not many people reading popular science today are willing to make such efforts, they prefer the feeling of having confronted something profound, and if it makes them feel good about themselves and their lifesyles, so much the better.
Anyhow, for what it's worth, that's my take.

reader Luboš Motl said...

I used to say the same thing - physics (and mathematics etc.) is more immune against fads etc. The communist party at my Alma Mater - math-phys faculty - was OK, the degree of Marxist penetration was low etc.

However, in recent years, I don't have the impression that physics - and I mean real-world physicists - is immune to similar fads and pressures.

reader RAF III said...

Lubos - Agreed. For obvious reasons it has just taken longer to undermine standards in physics or mathematics as opposed to, say, literary criticism.

I am more optimistic about the survival of such hard sciences than I am about any of the humanities. Six or seven years ago my wife bought two sets of DVDs for our son - Civilization by Kenneth Clarke and The Ascent of Man by Jacob Bronowski. Watching them again after forty years it struck me that both were products of a vanished culture.

reader John Archer said...


If you didn't know already and your blood pressure can stand it I have some news for you. Brace yourself:

Al beeb is doing a remake.

Hello! I hope you're still OK.

Anyway, I think we can all imagine that's going to be like.

As one commenter (a Mr Jim Jordan) said on this piece in The Spectator (Why the BBC will never match Kenneth Clark’s Civilisation):

"I don't think a remake would be "eminently boring". I think it would be full of "progressive" doctrines of tolerance, diversity, pluralism, multiculturalism, inclusiveness, egalitarianism, feminism, homophilia, etc etc. The proper response to this is not boredom but rage." [My emphasis]

reader RAF III said...

John - Yikes! No need to worry about my blood pressure, thanks. My immediate reaction was to laugh out loud. I remain optimistic. This remake could be one of the funniest things ever.

reader twinings said...

So you agree now that Ukrainian government is not "fascist" or "Nazi" or "hunta", as you and kremlin was saying once... Neither of the nationalistic parties passed to the new parliament.

What do you mean that "Novorussia" didn't vote?
There is no such thing as "Novorussia" and the small part of the occupied Donbass actually did vote. They mainly voted for "Opposition party" (former party of yanukovich). This is why they took so many votes.

Today's elections in occupied territories are of-course illegitimate and the result will be totally faked. Already more than 40.000 people voted through internet :)

Also have a look at the list of european "observers" at today "elections":

Communists together with fascists who are putin's puppets.
Not surprisingly...

reader Luboš Motl said...

No, I don't agree.

reader twinings said...

Here's an example of today's "elections" in Donetsk:

In the following picture you can see elections in Kiev (left, Ukrainian prime minister Yatseniuk waiting in queue to vote) and in Donetsk (right, prime minister of DNR Zaharchenko goint to vote)

Another video showing a "court" in "Novorussia", where people are voting for execution of a man who is supposed to had committed a crime.

The real junta and fascists are in "Novorussia", not in Kiev. I don't know what else I need to do in order to persuade you....

reader Ray said...

The Obama administration has been filled with incompetent women.