## Thursday, February 27, 2014

### Stringless, recursive calculations in string theory

Rutger H. Boels and Tobias Hansen of DESY, Hamburg released a very interesting 66-page-long hep-th preprint today,
String theory in target space
They are effectively generalizing the Britto-Cachazo-Feng-Witten (BCFW) techniques from the case of quantum field theory (gauge theory) to the case of perturbative string theory.

Slightly off-topic. Congratulations to Joe Polchinski who will be 60 in the spring but who already has the Joefest now; see Clifford Johnson and Matt Strassler. If you need a higer-res version of the picture, let me know.

One may say – and they probably say – that they're returning to the mode of reasoning that existed shortly after the birth of string theory (the publication of the Veneziano amplitude) before it was shown that Veneziano's amplitude followed from a theory of strings.

Once this "constructive" derivation of the amplitudes was found by the co-fathers of string theory such as Nambu, Susskind, and Nielsen, string theorists largely abandoned the string theory's roots in the "S-matrix program". This program – whose original emergence traces back to Werner Heisenberg – became unfashionable once both the QCD and string theory's amplitudes were derived from a very particular set of degrees of freedom (quarks and gluons; strings) and a particular Lagrangian.

Against the spirit of the S-matrix program and the bootstrap paradigm, the internal consistency ceased to be "fundamental"; it could have been derived from the defining conditions.

However, these two researchers in Germany show that many still unknown or overlooked "not constructive" or "S-matrix-consistency-related" insights about string theory may be waiting – a whole machinery to reinterpret all the calculations in which strings and their 2D world sheets don't look central at all. If true, these are the stringy counterparts of the S-matrix flavor that was revived by the recent twistor minirevolution in the context of gauge theories.

Their main technical foci of interest are roots (zeroes) of the scattering amplitudes, effectively coming from the poles of the Gamma function in the amplitudes' denominators. Note that normally we only know where the poles of the amplitudes, i.e. poles of the Gamma functions in the numerator, come from. They come from virtual particles in the processes.

But they use some Plahte's 1970 insights about the monodromies of the amplitudes under the permutations of the external particles, see e.g. a 2010 paper by Boels et al., to write down the amplitudes differently.

They show the unitarity of the S-matrix in a new light. Unitarity relates the loop amplitudes to the tree-level amplitudes, among other things. It's possible to prove it (and the no-ghost theorem about the positivity of residues etc.) using the world sheet construction – a strategy of the proof that isn't really useful for a direct, alternative calculation of the loop diagrams. But they effectively achieve the same outcome without any world sheets, using BCFW-like tricks extended from field theory to string theory. And they reduce the proofs of some mathematical claims about the positivity of some sums that don't seem to be "manifestly stringy" in any sense.

There are many recursion relations that one may write down for the stringy scattering amplitudes. They're not quite independent and they argue that the old-fashioned string duality (currently known as the "world-sheet duality") relates these different recursion relations with each other. Closed string amplitudes are mostly obtained by the KLT (closed equals open squared) relations in this paper.

I don't quite understand how it works so far but I do believe that it may be a good idea for experts among the TRF readers to spend some time with this preprint and its references. It seems to me that in the future, people will understand the power of internal consistency much more intimately than today. They will know that whole S-matrices or their subsets (by the number of external particles or loops or other labels) follow from consistency and a few assumptions. Ideally, sometime in the future, people should be able to rigorously, mathematically prove that a "consistent theory of quantum gravity" and "string/M-theory" are really two descriptions of the same thing. I view S-matrix-program-based advances such as this paper to be steps in this direction.

eXciting dark matter

Just two more sentences. Dark matter top experts Douglas Finkbeiner and Neal Weiner released An X-Ray Line from eXciting Dark Matter where they try to explain the 3.5 keV line not by a 7 keV sterile neutrino but by a decay $$\chi^*\to \chi+\gamma$$ between two nearly degenerate states $$\chi,\chi^*$$ of the dark matter, while the decay is mediated by the field $$\phi$$.

The particle may also be a 7-keV string-theoretical modulus, i.e. scalar field describing the shape of extra dimensions etc., according to a paper released tomorrow.

Justified or not, the use of the Nazi term is just a way to "succesfully" respond with something to those that only provide insults and therefore cannot be responded with anything else. Noticed the double quotes? If anything, you will only be succesful... in a war of insults. And only be considered succesful by whoever was already on your side initially. Which is infantile and obtains nothing.

2. Dear Nylo, there have been lots of insults. However, apologies if you disagree but I don't consider the observations of the analogies between the Nazis and the global warming fearmongers to be instults at all. They are observations of genuine similarities, ones that may have as dark consequences as those in the Nazi era, and I find detailed analyses of these similarities between these two political movements to be profound enough political science. This is the primary thing contributed to e.g. by the Czech ex-president Václav Klaus.

Just because the word "insult" is sometimes used on both sides doesn't mean that both kinds of comparisons are equally justifiable. They're not. Climate skeptics generally have nothing to do with the Nazis while the climate fearmongers have lots and lots in common with the Nazis.

3. So, do you mean that when Spencer wrote "somebody pushed my button", or "Too many of us for too long have ignored the repulsive, extremist nature of the comparison. It’s time to push back. I’m now going to start calling these people global warming Nazis” because of feeling insulted by the denier term, he was not pretending to make the other side feel insulted as well by the use of the Nazi label? An insult is what you say in order to make the other person feel insulted, regardless of whether it is accurate or not. That's why "black" or "nigger" when told to an afroamerican is considered an insult, for instance. It's not the term, but what it provoques in the person that receives it. Whatever adjective you use in order to annoy the other person, is an insult.

4. I don't see into Spencer's head. Some experience may have been the last droplet for him. However, Spencer didn't mean to use the term just once. He said that he would be using the term as long as the denier term would be used by the global warming Nazis.

At any rate, I am not Spencer but I can tell you what I think. I think that the explanations of the similarities between the two movements are important and accurate whether someone feels insulted by them or not.

5. Maybe you are aware that the "snake's egg", as we say in greek, has hatched, and a Nazi party called "golden dawn" wit a fuhrer and everthing and around 10% power in the polls is in our news.

They are ultranationalist, against immigrants , particularly of color, glorifying the paganism of ancient greece and all sorts of that nonsense. They are being prosecuted because expelled members have talked and given videos etc where you see their fascist organization and their nondemocratic goals. Half of their Mp's are in jail and there exists a request for waving MP immunity for the rest. One cannot believe that adults , mostly men but also some women, want a leader and army discipline to rule their life, but they do. They march and shout and do all sorts of stupid things which have been recorded and enrich our nightly news :(. Curiously they do not particularly target the Jews, I guess because the immigration problems in the new ghettoes of Athens and large cities loam huge on the populace and gathers them followers.

I guess people in groups have not advanced much more than wolves in packs : they need a leader and once the hierarchy is fixed they are happy to be followers. Come to think of it, football fans are as fanatic and mindless up to hooliganism against other teams' fans. All it would take is a charismatic leader to channel all this mindless adrenaline and testosterone into fascism :(. Well, economic straits too, as has happened in Greece where we had . This is very strange since hundreds of thousands of civilian greeks died during the occupation , let alone the villages where all men were killed and villages razed to the ground. Even so, in Crete there exists a fascist following, a reagion where one can still see the plaque the german overseer set up where the village of Kandanos was burned to the ground ." here was Kandanos" .

Maybe we are lucky that no strong leader has appeared in the global warming community to unify them, though politicians have sensed the potential and try to rally the troupes. Fortunately the troupes are still at a random walk with some collective AGW component. If the US gets a second winter like this, I foresee the AGW motion will stall..

6. historical journey is interesting

7. The hard-core leftwing including climate alarmists want to control language, political correctness attempts to rein in expression and thus thoughts and propositions people can ponder and discuss. It is a pure totalitarian power grab. They want to imprison thoughtful opposition to their blunt ideology by incessant use of manipulative, misleading slogans such as 'climate denier'. It must be challenged at every opportunity, ridiculed and exposed for what it is.

8. Wow, Anna, this is really dark news. What a species we are. Well there are some bright beacons out there, thank goodness for TRF.

9. Anna, are "golden dawn" AGW, sceptics or deniers ?

10. Equal rights demands a Nobel Prize in each category for each defined minority lest elitist patriarchal White Protestant European capitalist colonialism be supported. Jews, with near no population statistics at all, comprise 30% of Nobel Laureates since 1900. Jews are disqualified as a minority given proper minorities like 1.1 billion Black Africans and 1.6 billion Muslims with their defining annual aggregate nothings.

The only 21st century sin is pulling your own weight. The criminal sentence for that is taxation for life. (If sunspot AR 1990 pops another fat X-flare in the next ten days, taxpayers are paroled.)

11. Shelley Rose finally comes out.

Congregations Caring for the Climate – Atlanta, GA

with Shelley Rose

http://www.flickr.com/photos/stepitup2007/464126698/

12. they probably know nothing about it. they are into guns and drills

13. So much of understanding these advanced topics is understanding the jargon -- such a simple thing as the Poincaire group once it is explained -- which is worth a lot even if one has not learned to speak "the language of mathematics." Personally I didn't get past modern algebra and introductory calculus -- to bad, cause I loved numbers back then!

14. "Due to their certain stronger abilities that are statistically
demonstrable, Jews play a disproportionately strong role in natural
sciences, banking, trading, U.S. foreign policy, and lots of other
things"

I think the banking one has more to do with historical reasons: namely that Christians were religiously prohibited from lending to one another at interest (Jews could lend to Gentiles at interest, but not each other). I think the evidence that this is the case is probably that the dominance in this case is certainly nothing like it was hundreds of years ago, when it was basically a monopoly. It took a long time but finally someone in a Christian culture said "wow you know, the prohibition against usury is really stupid."

Anyway, Lubos, other than that I completely agree with basically everything in this post.

15. In particular, the events in Ukraine have mostly nothing to do with the Jews, either.

Dear Luboš, I'm pleased to see you write that, because earlier I got the impression that you had fallen for the propaganda of the pro-Russian side in Ukraine's recent upheavals, which has cynically used accusations of antisemitism as a brush to smear the other side... while not being immune from such taint itself.

Indeed, events in Ukraine are not about the Jews, even though one could find small numbers of them on either side: the pro-Yanukovich camp and the Maidan protesters. Small numbers, because they are a tiny minority in Ukraine nowadays, far behind ethnic Ukrainians, Russians, Tatars, Moldavians, Poles, Romanians, Armenians, Byelorusians, Lithuanians...

(However, in recent years Hasidic Jews have been moving "back" to Ukraine (the cradle of Hasidism) to grow kosher wheat and bake kosher bread... but not in numbers to make them a factor in the economy.)

No, this time of change is first and foremost about the two major camps in Ukraine and whether they can find a way to get along with each other. The repeal by Ukraine's parliament of the language law that gave communities where at least 10 percent of the population speak Russian the right to make Russian an official language was a singularly boneheaded move. The decent, reasonable Ukrainians need to gain control over the knuckleheaded mouthbreathers in their midst and show some love to their Russian and Russophone compatriots.

16. Maybe, Werdna, although I would be impressed if this overrepresentation explained by this historical reason survived the centuries in which we Gentiles knew the concept of the interest already. ;-)

17. Lubos, you have just provided the PC police with the new term for "African americans" or "people of color" or whatever the current evolution of it is===
"low-albedo americans".
Our native Canadians have evolved from "Indians" after Columbus'(apparent) misattribution, to the current "First Nations people", and Eskimos to "Inuit", if I am not behind the times.
BTW, the Quebec government just sent its language police to tell a small clothes store owner that her Facebook page has to be changed from English to French or she will be fined. This is not local advertising and Facebook is not a Quebec company. Now Quebec is trying to control the internet. Their language police are farcical, but then, they are French :)

18. Even though I have some more socialist views than most in the US, you are absolutely right, Ann. The hard core left and the hard core right are equally ridiculous, but the leftwing are definitely the language police.
While they claim moral superiority in promoting individual rights, they use fascist tactics, smears, ad hominem attacks to bully and intimidate. These people, in their zealousness, are either immoral, or sociopathic, or both. I have actually heard very few insults flowing from sceptics to AGW promoters. Sceptic is not "denier". I actually doubt that there are very few deniers, but the AGW brigade constantly attack the straw man "denier". Yes, Al Gore, the truth is "inconvenient", it is just that you have distorted it using your reality distortion field.
The hard core AGW people use the Bellman's Rule of Three---"Anything I say three times is true." (Hunting of the Snark-Lewis Carroll).
Yes, the climate is changing. Yes humans have some part in this. I do not personally know of any sceptics who do not believe this. The kicker is in the action required (or not). Even James Lovelock says that humans can do nothing that will benefit. While I don't agree with this, bankrupting countries and enriching Gore and Pachauri and other opportunists and sociopaths does not resonate with me.

19. I think this Christian prohibition against moneylending was more often honored in the breach.

If you look at Christian-owned and run banking houses such as the Medici, the Welsers and the Fuggers, they don't seem to have had many qualms about extending credit for profit, nor much trouble from the Church.

The Fuggers, and arguably the Medici also, were in their heyday much richer and more powerful than the Rothschilds centuries later.

This painting is amusing for the stories that have been told about it at varying times.

It depicts Jakob Fugger throwing the IOUs (the debt certificates) that he held over Charles V into the fireplace, in the presence of the Holy Roman Emperor and his entourage.

A 19th-century German writer claimed that this was a record of a historical episode when the Fuggers had advanced to Charles V substantial sums of money for his joint campaign (with the French) against the Turks, a war that culminated in the siege of Tunis from the sea in 1531 and ended in victory and with the freeing of twenty thousand Christian slaves. Such was the heroism of Charles and the magnanimity of Anton [sic] Fugger that the latter invited the Emperor to his home and in his presence spontaneously burned the title to repayment of the debt (which he could afford, being richer than Croesus).

Later scholarship insisted that it was Jacob Fugger ("the Rich"), not Anton, and that the debt being forgiven had nothing to do with the campaign against the Turks. According to one 20th-century author, Jacob Fugger had been instrumental in deposing Sigmund the Habsburg archduke of Tyrol, who was unable to pay the Fuggers the money he owed them, and had him replaced with Maximilian, another Habsburg, who subsequently became the first Holy Roman Emperor. Maximilian granted the Fuggers privileges that made them breathtakingly rich, from the silver mining and copper monopolies to banking, arms manufacture, land ownership, and administratorship of coinage.

However, Maximilian's debts kept mounting and when he died, the Fuggers had to shell out several hundred thousand guilders to bribe the Electors into voting for his son -- Charles V.

In the meantime the Fuggers had also organized the selling of indulgences on behalf of the Vatican, the excesses of which led to the Reformation. They would also finance the Counter-Reformation and the suppression of peasants' revolts. However, at some point they miscalculated and their sovereign debtors -- above all, Charles V -- gained "debtors' leverage" over them. (The heads of state also had the useful ability to put the thumbscrews on their bankers by restricting their business if the bankers did not meet their demands for ever more loans.)

So in the end, the Fuggers did have to write off a huge fortune as Charles V resigned the crown in 1556 and his successor Philip II declared his state bankrupt. However, the episode with the burning of IOUs, although it makes for good drama, is apocryphal.

In 1978, when the 17th generation Fugger patriarch was interviewed, he said that the receipts had never been burned -- and that the Habsburgs then owed his family some 250 billion deutschmarks (including interest).

Hope you don't mind my historic digression.

20. Well spoken, Gordon. I wish we could move away from the phrase 'climate change' because it is so uninformative. How about 'climate oscillations' or 'climate cycles' or 'climate anomalies' Make them define what scale is being discussed (15 years, decades, centuries, millennia, etc.) If you spit in the ocean it changes the sea level, I suppose, but it's a ridiculous scale to consider for most purposes. But AGW seem to be obsessed with spit in the ocean and on that basis pushing for ruinous economic policies, as you point out. My AGW neighbors read the daily weather like tea leaves, i.e., unpleasant weather events become signals, warnings from Mama Nature. it's quite disconcerting.

21. Hm, perhaps not.

Certainly wouldn't be the first time I've been wrong.

22. Come on Gordon you are just jealous that these Canadians speak French too?

23. Hi Eugene, I hope you will take a re-look at that comment you made about me and anti-Semitism and in particular my reply to it and my reply to Shannon's comment, and that you will then withdraw your insinuation as contrary to all the evidence. I would deeply appreciate that as unjustifiable insinuations about my moral character are . . . well, just plain unacceptable. I post under my own name on the web always, never anonymously, and my reputation means a lot to me at least and (who knows?) maybe others too. thanks in advance, Luke

24. There's a whole concept here https://en.wikipedia.org/wiki/Ashkenazi_Jewish_intelligence. It seems that ''Jews play a disproportionately strong role in natural sciences, banking, trading, U.S. foreign policy, and lots of other things'' due to higher average IQ. This, however, only concerns Ashkenazi Jews, not other Jews.

25. Hi Luke, if you want me to reconsider my decision not to engage in dialogue with you anymore, you will please first

(1) unequivocally and irrevocably withdraw your present threat of taking legal action against me and
(2) commit yourself to not take legal action against me at any time in the future for anything I may say here (i.e., on TRF) to you or about you.

I will of course extend the same courtesy to you, i.e., commit to not take legal action against you at any time in the future for anything you may say on TRF to me or about me.

26. You can see as major reason that Jews were often restricted from land ownership. Thus, while most of the society worked jobs related to agriculture, and later industry Jews worked jobs not requiring to own any land: sciences, banking, trading, medicine, ...

27. If you will honestly reconsider based on the evidence -- no promise of your conclusion required in advance -- then I will withdraw any threat of legal action. In fact I here now withdraw it.

28. Peer pressure -- the desire to fit in, to be accepted by one's friends and colleagues -- turns out to be one of the most powerful forces in the world, or at least so I have concluded in my old age. It is far more powerful than reason or evidence.

They say that sociopaths are born that way, that through some genetic quirk the part of their brains that are responsible for human empathy just aren't there. I don't know if that is true or not. But if there is a similar area of the brain that is responsible for conformity, especially conformity of opinion, then I suspect that I was born without it. Based on the evidence I'd say Lubos was too. ;)

29. Hbd*chick refers to it as left-wing authoritarianism. She analyzes it at length on her blog.

30. Shannon, I speak and read French also, not fluently, but generally acceptably sans l'accent joual.

31. Dear Motl,

Thanks. I am reading that famous paper.

I mentioned AdS4/CFT3 is to set a situation that the difference of two roots is positive integer, such as $m^2 = -2; d = 3$. I can grasp when the two exponents are the same( the difference of two roots is zero), the logarithm problem need to taken into account, however , what about when the two roots differ by an positive integer? Without any extra treatment, I thought the log term would happened in this case. Am I right for this view?

However, in such case, those log part in asymptotic behavior are not really cause physics since we have some procedure to cope with them. so we can neglect them.

Do I misunderstand something?

Thank you a lot.

henring

32. Right, that's what I meant: m^2 must be a *particular* integer for a given dimension for the logarithm to arise.

Only particles beneath the BF bounds are "real" tachyons with the instability, and they're prohibited by consistency. The BF bound itself where the logarithm appears is marginally allowed, and physics of that may be obtained by thinking about the limit of the power-law case, so there won't be any problem.

33. my question is about the case two roots different by a positive integer, a logarithmic part will arise in asymptotic behavior, but even so, we also can have two conformal field theory, because a treatment can heal the divergent caused by the logarithmic part. I read some papers, e.g. :http://arxiv.org/abs/hep-th/0209067

around (5.24), it seem that, the renormalization procedure deals with the divergence.

I am talking about the one-point function, because this function can be related to the asymptotic coefficients of the scalar field which are the $a, b$ in $\Phi = a z^{\triangle_-} + b z^{\triangle_+}+ ....$,

I think
1. the first term ;$a z^{\triangle_-}$ comes from the solution with logarithmic part,
2. the logarithmic part is neglected after renormalization, that is why we say the asymptotic behavior is $\Phi = a z^{\triangle_-} + b z^{\triangle_+}+ ....$
3. All conclusions is also valid when black hole taken into account.

I need to make clear the three problems.

Thank you for you patience.

34. Apologies, I don't understand the questions well enough.

35. sorry, may be my expression is not clear enough.

In short, in the case two roots differ by a positive integer, if the mass square of scalar field under BF bound, we also can have two conformal field theories, and needn't worry about the logarithmic term.

is the understanding appropriate ?

thank you again

36. O.K., thanks. I will give this matter some thought and get back to you as soon as possible, perhaps late this weekend.

37. Also check out this cool TRX workouts www.99suspensiontraining.com/

38. For fields more tachyonic than the BF bounds, the calculated dimensions are complex and complex conjugate to one another and the CFT isn't unitary, but it would still be one CFT.

39. Lubos, an insult is an insult regardless of whether it's true.

40. Great, Smoking Frog, but your sentence is just a worthless tautology. The truth is a good thing whether or not it is an insult.

41. Aaah :-) Dommage Gordon! L'accent Quebecois est charmant et amusant... parfois difficile à comprendre. I am genuinely happy that French is spoken on your side of the Atlantic and I support their efforts to protect our language. This has nothing to do with political correctness, it is just about saving a language and culture... I see it as a plus for Quebec.

42. I know it's a tautology. I just didn't think it worth the effort to explain the obvious, that an insult may be true.

The truth is a good thing whether or not it is an insult.

Sure, in the abstract, but it doesn't follow that stating the truth is always a good thing, and by this I do not mean that delivering an insult is always a bad thing. You seem to think that an insult should never be delivered.

43. I can't wait to see a movie about these Ukraine events too, and the way it will be depicted ie which side of the spectrum ;-)
I've read that Czech Rep might join the Eurozone within 2 to 5 years ? Oh jeez, hopefully it'll be too late by then ;-)
Oh and: Allez Pilsen!

44. "charmant"---hmm, ce n'est pas un mot juste :)
Nah, the language police in Quebec are ridiculous...the stories of their intrusions make Monty Python seem tame.
This was the woman's Facebook page---not signage, not advertising fliers. They violate human rights and many francophones in Quebec are appalled.
About the charming joual---it reminds me of the slackjawed lazy patois of deep south US accents. I can follow the French CBC news shows easily, but even you would be mystified by the bulk of the game show, soaps etc programming.
The language laws are entirely a creature of the Parti Quebecois, essentially a separatist party which, when it is politically convenient, goes into stealth mode. There are other pockets of French in Canada---mostly in the Maritimes, and, in all provinces, we take French in school from grade 1.(though that doesn't guarantee fluency) and parents have the option, even in BC of placing their children in French immersion.

45. Oh well, it is still nice for them to have both languages, isn't it? You know, in Ireland, Irish Gaelic is compulsory until you leave secondary school. It is as important as math and English. And the only place in the world where it is spoken is in the most remote places of the island... by a few people ;-). It is a nice language though, there is something romantic to it.

46. Dear Shannon, the odds of our joining the eurozone before 2020 are something like 10 percent.

47. @ shannon
They speak Gaelic much more in Wales. The place names and words are horrendously long.

48. Gordon, indeed the longest name of a village is Welsh: "Llanfairpwllgwyngyllgogerychwyrndrobwllllantysiliogogogoch"
However writing Gaelic on signposts doesn't necessarily mean they speak it everyday. Most signposts in Wales, Ireland and Scotland show both Gaelic and English. Same in Brittany: Breton and French. Actually all these Gaelic languages differ quite a lot. I only know of a few words that are the same in Irish, Welsh and Breton like "fire" is "tan", and the colour "black" is "du" (as in Dublin which means black pool). In Breton our flag is called the "Gwen a Du" (white and black), but "white" in Irish is "bán", whereas in Welsh it is "gwen" as in Breton.
All these regions are trying to keep their identity alive. It is purely cultural. I find it always exciting to find similarity between people, don't you? I would love to visit Quebec because I would feel like I am part of the family. It is a nice feeling.

49. The ADL, once a far more credible organization, has slowly been taken over by "liberal" Jews (the kind who vote for Democrats). But then, so have many other institutions these days. We have no shortage of confused and ideologically challenged children in positions requiring a maturity few possess.

In the case of the ADL. they've been brainwashed from the cradle, thinking they must support "liberal" causes, and oppose "right-wing" ones. Never mind that the most destructive movements have virtually always been "left-wing." They don't know that, any more than most scientific institutions these days do.

Yes, they are wrong, but they are not evil. And, I repeat, they are not alone. Sadly, there's all too much insanity going around. Science has not been immune. The rot is everywhere. So, before you get upset with Jews who don't know any better, I would suggest you fix the problems on your own turf first. In the end, they are the ones that will make the most difference, anyway.

Confused liberal Jews making a fuss over semantics, or scientists responsible for informing public policy. Which ones do you want to know what they are doing?

Rudyard Kipling suggested a reasonable way for a reflective man to measure his own maturity.