## Anomalies Revisited

Some of the talks at Strings 2015 have now appeared online, and one of them I found quite fascinating, Witten’s Anomalies Revisited. Some of his motivation comes from string perturbation theory and M-theory, but the questions he addresses are fundamental, deep questions about quantum field theory (and not just any quantum field theory, but exactly the sort of qft that appears in the SM, spinors chirally-coupled to gauge-fields/metrics).

The fundamental issue is that these are theories where the path integral does not determine the phase of the partition function. Part of story here is the well-known story of anomalies, perturbative and global. One interesting point Witten makes is that vanishing of these anomalies is not sufficient to be able to consistently choose the phase of the partition function, and he gives a conjecture for a necessary condition that is stronger than anomaly cancellation.

The standard story of QFT textbooks is that once a Lagrangian is chosen, the corresponding QFT is well-defined. But quantization really is a lot more subtle than that, and the anomaly phenomenon is just one indication of the problem. In earlier parts of my career I spent a lot of time thinking about anomalies; the connections to some of the deepest mathematics around (K-theory, index theory and much more) are truly remarkable. In recent years I’ve been thinking about other things, but Witten’s talk is a strong encouragement to go back and revisit the anomaly story (some of his best work has “revisited” in the title…)

In particular, Witten emphasizes a particular case I’d never paid much attention to: the 3d massless Majorana fermion. One would think that this is among the simplest quantum field theories around, but Witten explains how this is an example of a theory with a potential inconsistency (no way to consistently choose the sign of the partition function), even when the anomaly vanishes. This theory also appears in a hot topic in condensed matter physics, the theory of topological superconductors. One reference Witten gives to related work is to this recent paper (there’s a typo in his reference, should be 1406.7329 not 1407.7329).

Witten ends with:

I hope I have at least succeeded today in giving an overview of the tools that are needed to study the subtle fermion integrals that frequently arise in string/M-theory. A detailed analysis of a specific problem would really require a different lecture. Write-ups of some of the problems I’ve mentioned – and some similar ones – will appear soon.

I look forward to those write-ups, with the theories he’s talking about of a lot more interest than just their role in string/M-theory calculations.

Posted in Uncategorized | 9 Comments

## Convergence

Another conference that starts today is the Convergence conference at the Perimeter Institute. The concept is explained by Neil Turok here. His point of view is one I’m very much in sympathy with:

Turok explains that the “large bandwagon” of the last 30 years has not found experimental support. The bandwagon in question is the Standard Model of particle physics established in the 1970s, which, he says, people have been elaborating ever since. “Grand unified theories, supersymmetry, string theory, M-theory, multiverse theory,” he lists. “Each is not particularly radical, but is becoming ever more complex and arbitrary.”

To illustrate the lack of experimental support for these ideas, Turok describes how many people were hoping string theory would represent a radical development; but since string theory – as currently interpreted – leads to the multiverse, Turok describes it as the “least predictive theory ever”.

Indeed, experimental support has not been found for other extensions of the Standard Model either. “We have discovered the Higgs and nothing else,” says Turok, “yet the vast majority of theorists had been confidently predicting WIMPS (weakly interacting massive particles) and supersymmetric particles…Theorists are walking around in a bit of a stunned silence.” He adds that it could turn out to be right that all sorts of other particles are needed along with the Higgs – but that thought seems to be misguided.

“My view is that this has been a kind of catastrophe – we’ve lost our way,” he says. “What we need are ideas as simple and radical as in the start of the 20th century with quantum mechanics.”

So what might these ideas look like? Turok explains how observations have shown that the universe is simpler than we ever expected – in contrast to our theories, which are becoming ever more complex.

It’s great to see this, very encouraging to think that a more reality-based point of view on fundamental physical theory may finally be emerging. My only criticism is that the program doesn’t seem to include any mathematics or mathematicians (except perhaps in the context of history and Emmy Noether). If you have a structure you don’t understand, which is unusually simple, with surprising explanatory power, you might want to ask mathematicians about it…

The schedule is here, there’s a blog here.

There is no difference that we know right now … between the story of divine intervention and the multiverse.

It’s great to see a conference on fundamental physics where the multiverse is coming in for some appropriate skepticism.

Update: One thing to say about the multiverse, it does provide an excuse for an endless number of popular articles mulling it over. Just today, there’s Caleb Scharf and George Johnson.

Posted in Uncategorized | 34 Comments

## Strings 2015

Strings 2015 gets underway in Bangalore tomorrow, and so far the press coverage I’ve seen consists just of two articles that aren’t what I’d guess string theorists would like to see:

• In The theory that may have been stringing scientists along for years Robert Matthews starts with

Over the next few days, the southern Indian city of Bangalore will be playing host to an exclusive group of people.

No amount of money can buy you membership and it doesn’t matter how well connected you are. But rumour has it that it helps if you have a brain the size of a planet.

but soon moves on to

There’s just one problem: there’s not a shred of evidence to support it. And that is now leading to awkward questions about just what all these very smart people have been doing with their time and funding.

He then goes on to discuss the recent New York Times Op-Ed, as well as a Physics Today piece

The American Institute of Physics has now gone further, with an editorial in Physics Today asking if the insouciance of string theorists over the issue of testability may harm public faith in science.

Finally, there’s an accurate discussion of the relation of string theory to the search for superpartners in Run 2 at the LHC

The real fun and games will start if the particles are not found. That is because, even after all these years, string theory is not tied down very tightly.

As a result, theorists can tweak their equations to explain away the failure.

Such flexibility is a classic symptom of pseudo-science, and it is what particularly irks physicists about string theory – along with the arrogance of some of its practitioners, who insist it is the only way to complete Einstein’s quest.

But there is another source of resentment, and one with which we can all sympathise: that an entire generation of brilliant minds may have been lost to an esoteric mind-game.

• The other string theory news story is at The Telegraph, a Calcutta paper, which has Physicists too can have fun. The article is about Ashoke Sen’s bizarre hep-th article Riding Away from Doomsday, which was the topic of an April 1 posting here. Since then, Sen has shot down any idea that this was a hoax, and has turned it into a major research program, with a technical hep-th article and a talk scheduled for the opening session of the conference tomorrow. The article argues for the importance of computing the decay rate of the universe since it

is important for planning our future course of action if we are to adapt this strategy for increasing the life expectancy of the human race.

String theory is supposed to provide this calculation, but Sen characterizes the status of that calculation with

it is probably fair to say that we do not yet have a definite result based on which we can plan our future course of action.

which shows that, despite what some people say, he definitely has a sense of humor.

Given press coverage debating whether string landscape research is pseudo-science or a joke, I wonder what prominent string theorists gathered in Bangalore now think of the string theory community’s decision over the last ten years to mostly go along with the idea of the string landscape as an excuse for why string theory predicts nothing. This all started about ten years ago, and it’s interesting to take a look again at the panel discussion at Strings 2005, where the panelists were in favor of the landscape, but the audience not so much. The last ten years have shown conclusively that any hopes for predictive science coming out of the landscape were misguided, but will that or bad press cause anyone to re-evaluate their stand on this?

Update: Slides of the talks are appearing here. One of them is so interesting I’ll devote a posting to it…

Posted in Strings 2XXX | 16 Comments

## Multiversal Journeys

One of the many efforts to promote the Multiverse to the public way back when (2005-2007, some of their advertisements are here) was an organization called Multiversal Journeys. Back in 2006 they got $77,000 in funding from the Templeton Foundation (via FQXi). Since 2007 they seemed to have disappeared, with no more scheduled public events as far as I could tell. Now they’re back though, with an upcoming event defensively called Clarifying theoretical physics and cosmology misconceptions for SF Bay Area journalists. It’s unclear exactly what they think the misconceptions are that such journalists need to have clarified. One of the three announced speakers (John Terning) might actually be able to do some clarification, but the other two seem more devoted to the spreading of misconceptions. Yasunori Nomura likes to promote the idea that the landscape and the many-worlds interpretation of quantum mechanics are one and the same thing (see here and here), a claim I believe few serious physicists have ever been able to make sense of. He also claims that the multiverse can be used to make predictions about physics, and back in 2009 used the multiverse to predict that the Higgs mass would be 141 +/- 2 GeV (see here). This prediction played a central role in the film Particle Fever, which featured David Kaplan and Nima Arkani-Hamed during the period leading up to the Higgs discovery explaining how a 140 GeV Higgs would mean the multiverse was right. Will Nomura clarify for the journalists any misconceptions they might have about what scientists are supposed to do when their theory’s well-publicized prediction is tested and shown to be wrong? The other speaker is Texas Tech chemist William Poirier, who has some sort of “Many Interacting Worlds” theory, which supposedly shows that the observed behavior of particles indicates the existence of parallel universes (see here). Again, I’m curious what misconceptions about physics he plans to clarify to journalists. Update: I see that this event will be funded by at$5750 grant from FQXi to Multiversal Journeys (Fall 2014 Mini-grant).

Posted in Multiverse Mania | 23 Comments

Ordered from the more to less serious…

• On the geometric Langlands front, there’s video posted today of this talk by Dennis Gaitsgory. Michael Harris has already commented here about the local geometric Langlands conjecture in terms of 2-categories that Gaitsgory discusses. Today’s arXiv listings have a new paper on geometric Langlands by Witten, which begins with his version of a formulation relating the categorical point of view and quantum field theory.
I wrote recently here about a talk by Jacob Lurie that alluded to an explanation of this categorical equivalence for the simplest case of G invertible complex numbers (rather than the case of G a general semi-simple Lie group that Gaitsgory and Witten are discussing). I’m still far from being enlightened concerning that simplest case, but have learned a lot from Alexander Polishchuk’s Abelian varieties, theta functions and the Fourier transform which I take as treating the global versions of this equivalence.
• Witten has been busy, with yesterday’s arXiv listings including a 429 page paper with Gaiotto and Moore (does anyone know of a longer hep-th paper that’s not a review article?). There’s also a companion shorter summary paper. The motivation here is again a categorical picture expressed in terms of quantum field theory models, but for more insight you’ll need to find someone more expert than me on this topic.
• Strings 2015 will be held in Bangalore in a couple weeks. Talks titles are now available, so you can see what the hot topics in the “string theory” community are. Of Gaiotto, Moore and Witten, only Witten will be speaking. Perhaps his talk on An Overview of Worldsheet and Brane Anomalies will shed some light on the 429 page paper.
• On the Mochizuki/abc front, hopes rest on a planned workshop at Oxford this December. Fesenko has circulated a letter about the workshop, which gives suggestions about how to approach the subject.
• Via Chandan Dalawat’s Google+ page I found out about this autobiographical piece by Misha Gromov. One thing it made clear to me is why I couldn’t get anything out of the couple times I’ve heard him lecture.

Being trivial is our most dreaded pitfall: you say stupid things, not original things, outrageously wrong things – all will be forgotten when the dust settles down. But if you pompously call a+b=c “Theorem” in your paper, you will be forever remembered as “this a+b guy”, no matter you prove bloody good theorems afterwords…
I was introduced to the idea on September 1st 1960 at the then Leningrad University when our analysis professor Boris Mikhailovich Makarov said to me after our first calculus class – he expressed this in somewhat metaphorical terms – that I should’ve kept my mouth shut unless I had something non-trivial to say.
Further encouraged by my teachers and fellow students, I tried to follow his advice and, apparently, have succeeded – I hear nothing disrespectful about my mouth for the last 10-20 years. Strangely, this does not make me feel a lot happier.
“Trivial” is relative. Anything grasped as long as two minutes ago seems trivial to a working mathematician.

Another thought this raises is that I’ve just spent the last 3 years of my life writing something trivial

• I really like Jordan Ellenberg’s suggestion of Cold Topics Workshops.
• Mathematics makes it into the Guardian with an article about mathematical modeling.
• With the LHC inactive, some LHC physicists have had to spend their time studying plots (trigger warning, and NSFW).

Update: One more, far more serious than anything above. Sabine Hossenfelder brings up an important and rarely discussed topic here.

Posted in Uncategorized | 16 Comments

## CMB@50

Last week Princeton hosted what seems to have been a fascinating conference, celebrating the 50th anniversary of studies of the CMB. Hopefully videos and slides will be posted, but one can get some idea of the highlights of the talks from live tweeting that was going on, that is gathered together here. The third day of the conference featured a panel where sparks flew on the topics of inflation and the multiverse, including the following:

Neil Turok: “even from the beginning, inflation looked like a kluge to me… I rapidly formed the opinion that these guys were just making it up as they went along… Today inflation is the junk food of theoretical physics… Inflation isn’t radical enough – it’s too much a patchwork. It all rests on rare initial conditions… Akin to solving electron stability with springs… all we have is proof of expansion, not that the driving force is inflation… “because the alternatives are bad you must believe it” isn’t an option that I ascribe to, and one that is prevalent now… inflation is pretty but we should encourage young to think about its problems & be creative (not just do designer inflation)

David Spergel: papers on anthropics don’t teach us anything – which is why it isn’t useful.. sometimes we need to surrender (to anthropics) but that time is not yet now.

Slava Mukhanov: inflation is defined as exponential expansion (physics) + non-necessary metaphysics (Boltzmann brains etc)… we should separate inflation from the landscape… exponential inflation is very useful, the rest [of the metaphysical stuff] is not for scientific discussion… In most papers on initial conditions on inflation, people dig a hole, jump in, and then don’t succeed in getting out… unfortunately now we have three new indistinguishable inflation models a day – who cares?

Paul Steinhardt: inflation is a compelling story, it’s just not clear it is right… I’d appreciate that astronomers presented results as what they are (scale invariant etc) rather than ‘inflationary’… Everyone on this panel thinks multiverse is a disaster.

Roger Penrose: inflation isn’t falsifiable, it’s falsified… BICEP did a wonderful service by bringing all the Inflation-ists out of their shell, and giving them a black eye.

Marc Davis: astronomers don’t care about what you guys are speculating about at all (mulitiverses, pre-big bang, etc).

I was encouraged by Steinhardt’s claim that “Everyone on this panel thinks multiverse is a disaster.” (although I think he wasn’t including moderator Brian Greene). Perhaps as time goes on the fact that “the multiverse did it” is empty as science is becoming more and more obvious to everyone.

Posted in Multiverse Mania | 15 Comments

## A View from an Ex-String Theorist

Every so often I’ve taken a look at something about theoretical physics on Reddit, generally ending up not spending much time there. One reason was that I realize I’m already spending more of my life than is healthy arguing with people about string theory and the like, so better to avoid a new venue for that. The temptation to respond is strong when one sees someone mischaracterizing one’s opinions, but I’ve generally been able to resist temptation at that site.

Today I happened to come across a really wonderful discussion there though, and wanted to draw attention to it, even though it’s from a year ago. It’s entitled A View from an Ex-String Theorist and consists of a long piece by someone who has recently left string theory, as well as some answers to questions asked by others. If you want to understand what string theory looks like these days to good theorists who are working on it, read what “No_More_Strings” has to say.

No_More_Strings explains very well the difficult job situation in the field, and the effects this has. With a lot of very smart people and almost no jobs, postdocs are in no position to take the time to try and learn something new that isn’t a “hot topic”, or try and work on an unpopular idea that might take years to go anywhere. This is a huge part of the story of why this field is in trouble, and the situation seems to have just gotten worse since I wrote about it in my book over 10 years ago.

The suggestion that “string theorists” should stop calling what they do “string theory” is an excellent one. No_More_Strings explains how smart people in the field are not working on string unification, but have moved on to different things with little relation to quantized strings. Giving up the name would be a good first step to allowing people to think of what they are doing in a less narrow way. If you didn’t have to start every grant application by explaining that you’re motivated by “our best hope for a theory of everything”, you might find it easier to work on something quite different, with no relation at all to quantized strings.

I can’t quite resist correcting a couple things mentioning me. No, I don’t think string theorists are stupid. No, I don’t think that Witten “singlehandedly destroyed the study of “real” physics” (the last one isn’t the fault of No_More_Strings).

Posted in Uncategorized | 38 Comments

## A Crisis at the (Western) Edge of Physics

The New York Times had an op-ed piece this weekend by Adam Frank and Marcelo Gleiser, entitled A Crisis at the Edge of Physics. They make some of the usual criticisms of string theory and the multiverse, ending with

Are superstrings and the multiverse, painstakingly theorized by hundreds of brilliant scientists, anything more than modern-day epicycles?

I mostly agree, although I don’t think they make clear what the real problem is, that these theories predict nothing and explain nothing. In contrast, epicycles were a quite useful, well tested model that was highly predictive and approximately correct. If we had modern day epicycles, that would be a huge advance…

Last Friday in his concluding talk at a Nordita conference on particle physics and cosmology, Michael Turner gave his take on the multiverse:

Most important discovery since Copernicus?
Is it science? (not testable)
Many true believers (left coast) and not enough doubters.

He makes clear his opinion on these questions with this graphic:

and I think this expresses well the majority opinion of the physics community. A major question here is whether the problem of pseudo-scientific multiverse mania is one of the “edge” of physics (the “left edge”, as Turner notices and was discussed here), or whether it has infected the center. Some days I’m quite discouraged to see how widespread this is, other days it seems to me that we may finally be getting over this. There’s only so long you can get media attention for your empty but easy to understand new “Copernican revolution” before people lose interest and move on to something else. Perhaps we’re getting to that point. I think this was the first year that the World Science Festival here in New York didn’t have a program promoting the multiverse, and maybe that’s a sign of change.

For quite a few years now, there have been few scientific talks trying to use a multiverse to do calculations at serious string theory conferences (see for instance this week’s String Pheno 2015, or Strings 2015 later this month), with the multiverse mainly appearing in promotional talks to the public. Maybe the public is finally getting bored and starting to adopt the point of view that Turner’s graphic suggests (and that I think the physics community should get behind).

Update: Physics Today has an opinion piece entitled Could the evolution of theoretical physics harm public trust in science? This addresses an issue I don’t think some theorists realize the seriousness of. If you start arguing that conventional notions of testability don’t matter, this can be a very dangerous thing to do in an environment where public trust in science is an issue. Put differently, if physicists publicly promote the pursuit of speculative ideas in an ideological framework that can never be falsified, they create a real danger of a public perception that science is just one more ideology.

Posted in Multiverse Mania | 23 Comments

## The West Coast Metric is the Wrong One

I’m trying to get back to blogging about quantum mechanics slogans, this one is about relativistic quantum mechanics. I’m hoping it will stir up more trouble than my last East vs. West one.

If you’re doing calculations in relativistic quantum field theory, you typically handle the Minkowski nature of space-time by introducing an indefinite signature metric, and there are two possible choices:

• Mostly minus signs (for the spatial components), positive sign for the time direction. This is commonly known as the “West Coast metric”, I’m guessing because Feynman used it.
• Mostly plus signs (for the spatial components), negative sign for the time direction. This is commonly known as the “East Coast metric”, I’m guessing because Schwinger used it.

While I was educated on the East Coast, most courses I took and textbooks I used favored the West Coast metric, and that’s very much true of more recent textbooks (I don’t know of a recent one using the East Coast convention). When I started on this project I used the West Coast convention. After a while though, I finally found this conceptually more and more confusing, and switched to the East Coast convention. As time has gone on, I’ve become more and more convinced that this is the right convention to choose, that the West Coast convention is just a mistake, and a source of conceptual confusion in the subject.

Here are some reasons:

• With the East Coast convention, the treatment of spatial coordinates is just like in the non-relativistic case. In the West Coast convention, as far as space goes, you have decided to work with a negative definite metric, which is a quite misguided thing to do for obvious reasons.
• With the East Coast convention, if you do what you always do to make a QFT well-defined, analytically continue to imaginary time, you end up working with the standard Euclidean metric in four dimensions. In the West Coast version, you end up with a negative definite metric, again a bad idea (thanks to Peter Orland for emphasizing this to me). You could instead do your analytic continuation by analytically continuing all three of the space coordinates, also a really bad idea.
• With the East Coast convention, the Clifford algebra Cliff(3,1) is the algebra of real four by four matrices. In other words, you can choose your gamma-matrices to be real matrices and work with a real spinor representation (the Majorana representation). Going with the West Coast, Cliff(1,3) is the algebra of two by two quaternionic matrices, a confusing thing to work with. Ignoring that, what physicists end up doing is working with gamma matrices that are pure imaginary, which is highly confusing (odd powers of gamma matrices are pure imaginary, even ones real). According to Figueroa-O’Farrill, in this case you are working with:

pseudo-Majorana spinors – a nebulous concept best kept undisturbed.

To be fair, for this problem you can do what he does, and just change the sign in your definition of the Clifford algebra.

• Weinberg’s quantum field theory textbook uses the East Coast convention.

One reason this issue came to mind is that I’ve been trying to understand (not very successfully…) Schwinger’s old papers on Euclidean quantum field theory, where he makes some quite interesting claims. Schwinger used the East Coast convention for this, and as explained above, it’s only with this convention that you get something sensible after analytic continuation in time. There is very little literature following up on Schwinger’s arguments, I’m suspecting partly because in the West Coast convention following Schwinger’s arguments becomes virtually impossible.

The problem here is part of a more general problem, that I think most physicists don’t appreciate the mathematical concept of “real structure” or complexification. Given any formulas, they’re happy to just start using complex numbers, even when the quantities involved are real, with the idea that only at the end, when you get observable numbers, do you need to impose some reality condition. For an example of this, one often finds in qft texts claims that sound very strange to mathematicians, I have in mind especially things like

The mathematically sophisticated say that the algebra SO(3,1) is isomorphic to SU(2) X SU(2) (Tony Zee, QFT in a nutshell, page 113 first edition).

One problem here is that Zee is using the standard math notation for the Lie group to denote the Lie algebra, an unfortunately common practice. But the real problem is that the two Lie algebras are only isomorphic if you complexify, as real Lie algebras they are quite different. If you have always from the beginning complexified everything, this distinction doesn’t make sense to you, but it is often an important one if you want to really understand what is going on in some calculation involving spinors. For another example, there’s

the 3D rotation algebra, which has multiple names so(3)=sl(2,R)=so(1,1)=su(2), due to multiple Lie groups having the same algebra. So we have shown that so(3,1)=su(2) + su(2) (Matthew Schwartz, QFT and the Standard Model, Page 162).

Schwartz properly distinguishes by notation between the group and the Lie algebra, so is in better shape than Zee, but, again, so(3,1)=su(2) + su(2) is only true for complexified Lie algebras. The statement “so(3)=sl(2,R)=so(1,1)=su(2)” suffers from a typo (so(1,1) should be so(2,1)), but again an identification is being made that only makes sense if you have complexified everything. What’s really true here is that you have SL(2,R) a double cover of SO(2,1), and sl(2,R)=so(2,1), as well as SU(2) a double cover of SO(3), with su(2)=so(3). But SU(2) is a very different Lie group than SL(2,R) (although they share the complexification SL(2,C)).

So, my modest proposal is that the HEP community should just admit that the West Coast convention was a mistake, and rewrite all the textbooks (Weinberg doesn’t have to…).

Update
: A commenter tells me there is at least one recent textbook with the right convention, Srednicki’s.

Checking some books, I remembered one other intriguing recent choice, that of Michael Dine, who wrote the first half of his book (the QFT part) in the West Coast metric, but the second half (the string theory part) in the East Coast metric.

Update: For those interested in how to translate back and forth between Coasts in the two-spinor notation, I noticed that Dreiner, Haber and Martin have written review papers, with a line in the tex that lets you choose which Coast. See here and here.

Posted in Quantum Mechanics | 61 Comments

## LHC Run 2

Run 2 of the LHC is about to start with first stable beams scheduled for Wednesday morning, Geneva time). If you’re up (I’ll be asleep) you can watch a live webcast, or watch what is going on here. The current plan is 3 bunches/beam Wednesday, 13 bunches/beam Friday, and 48 bunches/beam over the weekend.

Tomorrow will also be an LHCC meeting, which you can also watch live. It will include reports from the experiments, and a status report about the machine which should give the latest details about the planned schedule for ramping up the intensity over the next couple months.

For the best advice about what to look for in coming months, see Jester’s summary here. First new results may well be about gluinos.

This week there’s a workshop going on at Nordita. On Thursday Gordon Kane will explain how string theory predicts that the LHC will see superpartners soon. I gather his claim is that gluinos are at 1.5 TeV, just above the Run I limits of around 1.4 TeV, so a sure thing for Run II. Of course, back in 1997 he was claiming they were at around 250 GeV, just above Run I limits, a sure thing for Run II (but that was the Tevatron…).

Update: Kane has very specific string theory predictions for Run 2: gluinos at 1.5 TeV, winos at 620 GeV (+/- 10%). So, I guess string theory is going to finally be tested by the LHC over the next year or so…

Posted in Experimental HEP News | 43 Comments