# String theory today

#### fzero

Homework Helper
Gold Member
I am aware of:
- no supersymmetric measure (like d4p in ordinary QFT) known beyond a few loops
- therefore no definition of higher-loop amplitutes
A measure on supermoduli space indeed exists and can be used to define all-loop amplitudes. The problem is that, except for small genus, it does not appear that the supermoduli spaces are split supermanifolds. Therefore there is no way to split the integration up into an integral over odd coordinates and an integral over even coordinates. The problem with higher-loop amplitudes is then a technical one: there is a definition, but we do not know how to evaluate the expression in closed form.

- no proof of finiteness of higher-loop amplitutes
For the bosonic string, modular invariance maps the region of geometries where UV divergences would appear to points in moduli space which correspond to IR physics. The bosonic theory has a special IR divergence due to the tachyon. The other potential IR divergences come from special points in moduli space where you have degenerate handles or punctures coming together.

In the superstring, the tachyon is absent. Furthermore, in the cases where supermoduli space is split, the integration over the odd moduli contributes to the measure over even moduli. We expect IR divergences to be related to the same phenomena as in the bosonic string. In the 1-loop and 2-loop vacuum cases, these divergences vanish after summing over the spin-structures. If the supermoduli space is not split, you can't sum over spin structures until you've integrated over the supermoduli. Witten's work is an attempt to investigate these IR divergences in this general case.

- no proof of convergence of the perturbation series
It's rarely the case that one expects a perturbation series to converge, rather perturbative series are asymptotic series. Even in ordinary QM, if we consider the harmonic oscillator with a $\lambda x^4$ perturbation, the radius of convergence of the perturbation series is zero.

#### Haelfix

Witten hinted he had a paper in preperation regarding details of the super Riemann surface at 2 loops, which did not use the same trick that Chen and Phong utilized.

Consequently its not hard to imagine that it might allow a new proof of the finiteness of the 2 loop amplitude and that further it might generalize more readily to the higher orders.

#### suprised

Witten hinted he had a paper in preperation regarding details of the super Riemann surface at 2 loops, which did not use the same trick that Chen and Phong utilized.

Consequently its not hard to imagine that it might allow a new proof of the finiteness of the 2 loop amplitude and that further it might generalize more readily to the higher orders.
Yes, his talk in the previous week in Bonn at the StringMath workshop was about that (improved understanding and construction of super rieman surfaces); I attended both talks. The first talk was more technical than the one in Munich and I found it more interesting. That applies to other some talks in Bonn, as compared to the ones of Strings 2012 as well.

But alas, what sense does it make to discuss this here.

#### tom.stoer

The problem is that, except for small genus, it does not appear that the supermoduli spaces are split supermanifolds. Therefore there is no way to split the integration up into an integral over odd coordinates and an integral over even coordinates. The problem with higher-loop amplitudes is then a technical one: there is a definition, but we do not know how to evaluate the expression in closed form.

...

If the supermoduli space is not split, you can't sum over spin structures until you've integrated over the supermoduli.
Thanks for the clarification. Is there a paper to understand the mathematical details of "split and non-split supermanifolds"?

It's rarely the case that one expects a perturbation series to converge, rather perturbative series are asymptotic series.
I know. But w/o an explicit calculation for strings it may be hard to guess the behaviour of the series.

#### fzero

Homework Helper
Gold Member
Thanks for the clarification. Is there a paper to understand the mathematical details of "split and non-split supermanifolds"?
I've never found a particular reference that I was completely happy with. Googling around now for free things, the lectures at http://www2.mathematik.hu-berlin.de/~groegerj/teaching_YO!_en.html#WS10/11:%20Super [Broken] seem ok and concise. Split supermanifolds are first mentioned in Lecture 4. For some directly relevant comments you might as well also read http://golem.ph.utexas.edu/~distler/blog/archives/000477.html.

I know. But w/o an explicit calculation for strings it may be hard to guess the behaviour of the series.
Yes, but the issue of whether it blows up at the 6th order or at the 12th is probably not physically relevant.

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#### tom.stoer

OK, seems to be a very subtle and rather unphysical issue. Nobody would ever calculate a 27-loop superintegtral even if the whole series would be finite ;-)

The question is why Witten addresses these issues today? What's the reason for the interest in these perturbative calculations?

#### suprised

Instead of agomizing about what he said or not and trying to read patterns in the coffee mug, why not just sitting back and wait for the paper to come out?

edit: well probably it is easier to read off the purported decline of string theory from the coffee mug, rather from actual research. So why dont you keep on going.

#### marcus

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Instead of agomizing about what he said or not and trying to read patterns in the coffee mug, why not just sitting back and wait for the paper to come out?

edit: well probably it is easier to read off the purported decline of string theory from the coffee mug, rather from actual research. So why dont you keep on going.
Hello S. it's nice to see you back and contributing to our discussions with your distinctive tone of voice!

I just tried the video link for David Gross's "Outlook and Vision" talk
http://www.theorie.physik.uni-muenchen.de/videos/strings2012/gross/index.html
and it did not work.
BTW on the overall list of video links it says a one-minute segment at the beginning of the talk is missing:
http://www.theorie.physik.uni-muenchen.de/videos/strings2012/index.html

Folks might want to watch some of Ooguri's "Conference Summary":
http://www.theorie.physik.uni-muenchen.de/videos/strings2012/ooguri/index.html
I just watched it. To the extent I could judge (not being at the conference) he did an excellent job. Highly informative, concentrated, fast, upbeat. He paraphrased Winston Churchill's speech "we shall fight on the X, we shall fight in the Y, we shall..." This fine paraphrase of of Churchill's morale-boosting determination in a dark hour came at minute 18 of Ooguri's talk. Strings 2013 will be at Seoul, 2014 in Princeton, 2015 in Bangalore. Ooguri gave a lightning montage of thumbnails of ALL the talks: lots of work went into the visuals and the delivery was excellent. Five stars.

I just tried again to get Gross's talk and it is still not coming up.

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#### lfighter

OK, seems to be a very subtle and rather unphysical issue. Nobody would ever calculate a 27-loop superintegtral even if the whole series would be finite ;-)

The question is why Witten addresses these issues today? What's the reason for the interest in these perturbative calculations?
You don't know what Witten is interested in and why. One month ago he wrote a condensed matter theory paper with Shou-Cheng Zhang and Xiao-Liang Qi(http://arxiv.org/abs/1206.1407). It's hard to predict his next move.

#### marcus

Gold Member
Dearly Missed
The Churchill speech that Ooguri starts paraphrasing at (or slightly before) minute 18 was given in June 1940 before the House of Commons. It was one of his finest and contained this passage:

"We shall go on to the end. We shall fight in France, we shall fight on the seas and oceans, we shall fight with growing confidence and growing strength in the air, we shall defend our island, whatever the cost may be. We shall fight on the beaches, we shall fight on the landing grounds, we shall fight in the fields and in the streets, we shall fight in the hills; we shall never surrender,..."

http://en.wikipedia.org/wiki/We_shall_fight_on_the_beaches

It was interesting that Ooguri thought necessary to use some of his time discussing the DEMOGRAPHICS of the string program: median age and national makeup of conference participants. He had prepared some bar-graphs and statistics.
=======================

It helps, I think, to make a clear distinction between the String program (consisting of people of a range of professional standing and interests, at various institutions) and String as a published body of theory.

Suprised used the word "decline". Of course the String program can decline (in terms of how much current research is cited, or in terms of new faculty hiring, or some other observable index) but this does not mean the body of theory declines. On the contrary, the body of published theory can only grow as more and more papers accumulate.

I suppose there could be questions of direction, or how focused current work is on the real problems of cosmology and the target areas that Tom mentioned. Direction focus and realness are somehow quality issues and our assessments tend to be subjective.

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#### atyy

Ooguri is funny. He says Hermann Nicolai exposed his secret spin foam past.

#### tom.stoer

You don't know what Witten is interested in and why.
That's why I am asking ;-)

String theory as of today suffers from many open issues; and I think perturbative finiteness is one of the minor ones b/c it goes away ones one understands its non-perturbative formulation in terms of unique fundamental d.o.f.. Therefore the question is if there's a strategy behind addressing these open issues, or whether this is simply fixing some minor problems.

#### xristy

Gold Member
In Witten's public talk during the Q&A he lists several discoveries like the Higgs and neutron starts that were viewed with skepticism and that took many decades to be discovered and then at 46:32 he says
Gravitational waves seemed hopelessly undetectable when Einstein first proposed - predicted them and the fact that eventually an incredibly story involving the binary pulsar made it possible to discover them was totally unforeseeable.
I've looked about but I don't see that LIGO or any other experiment has reported discovery of gravitational waves so I assume that Witten is simply suggesting they will surely be discovered but I'm not sure.

Have gravitational waves been observed or am I reading too much into Witten's statement?

#### marcus

Gold Member
Dearly Missed
In Witten's public talk during the Q&A he lists several discoveries like the Higgs and neutron starts that were viewed with skepticism and that took many decades to be discovered and then at 46:32 he says I've looked about but I don't see that LIGO or any other experiment has reported discovery of gravitational waves so I assume that Witten is simply suggesting they will surely be discovered but I'm not sure.

Have gravitational waves been observed or am I reading too much into Witten's statement?
A binary pulsar was observed to be losing energy at a rate consistent with the energy being carried off in the form of grav radiation.
I wil try to get a link for you.
I think that grav. waves have NOT been observed directly (as a periodic distortion of geometry.)

However the binary pulsar observation was widely accepted as proof that grav. waves are real. I personally was convinced FWIW. It seems to me smoking gun evidence.

You have two compact objects in rapid orbit and you time orbit precisely and you find it is SPEEDING UP.
So the two objects are spiraling in towards each other. They are losing energy. Where is this energy going?

Is there some kind of atmospheric drag? Well maybe that contributes somewhat but they are very massive very dense objects and you calculate that. You find it cannot be responsible for the main effect.

It is a beautiful idea that geometry itself could have a kind of "viscosity" and dissipate energy by carrying it away in the form of waves. I'll try to find the link (though I think you may know what I'm talking about already.)

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#### atyy

In Witten's public talk during the Q&A he lists several discoveries like the Higgs and neutron starts that were viewed with skepticism and that took many decades to be discovered and then at 46:32 he says I've looked about but I don't see that LIGO or any other experiment has reported discovery of gravitational waves so I assume that Witten is simply suggesting they will surely be discovered but I'm not sure.

Have gravitational waves been observed or am I reading too much into Witten's statement?
Maybe he is thinking about the indirect observation of gravitational waves by Taylor and Hulse's binary pulsar.

#### xristy

Gold Member
Thanks. I'm sure it was the indirect observation.

I noticed someone else recently referring to the indirect observation of the W in 1973 via the neutral current rather than referring to the decade later direct observation of the W.

#### marcus

Gold Member
Dearly Missed
Maybe he is thinking about the indirect observation of gravitational waves by Taylor and Hulse's binary pulsar.
Yes! for sure. I got a wiki passage that explains it adequately:
==quote Wikipedia==
The 1993 Nobel Prize was awarded to Joseph Taylor and Russell Hulse after they discovered two such stars. While Hulse was observing a new pulsar, named PSR B1913+16, he noticed that the frequency with which it pulsed fluctuated. It was concluded that the simplest explanation was that the pulsar was orbiting another star very closely at a high velocity. Hulse and Taylor determined that the stars were equally heavy by observing these pulse fluctuations, which led them to believe the other spatial object was also a neutron star.
The observations made of the orbital decay of this star system was a near perfect match to Einstein’s equations. Relativity predicts that over time a binary system’s orbital energy will be converted to gravitational radiation. Data collected by Taylor and his colleagues of the orbital period of PRS B1913+16 supported this relativistic prediction; they reported in 1983 that there was a difference in the observed minimum separation of the two pulsars compared to that expected if the orbital separation had remained constant. In the decade following its discovery the system’s orbital period had decreased by about 76 millionths of a second per year - this means that the pulsar was approaching its maximum separation more than a second earlier than it would have if the orbit had remained the same ...
==endquote==
http://en.wikipedia.org/wiki/Binary_pulsar

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