Comments on: News From The Front, III

By: News From the Front, IV - Asymptotia

News From the Front, IV - Asymptotia — Mon, 23 Oct 2006 01:09:11 +0000

[...] Before reading the paper -if interested- you can quickly refresh your memory of some of the context and technology I use by reading this post, and the papers referenced within. Why? Because: The theories are defined naturally by starting with models that yield wellâ€”understood string theories and allowing a fluxâ€”like background parameter to take halfâ€”integer rather than integer values. [...]

By: At The Monastery | Cosmic Variance

At The Monastery | Cosmic Variance — Thu, 06 Jul 2006 17:27:01 +0000

[...] The above example is a rare case -especially in higher dimensional or “critical” string theory- where an exact computation allows one to track the dynamics of the vacuum of string theory in an off-shell formulation. (It is possible in several cute toy models of non-critical strings in low dimensions, such as those I’ve described in other posts here and here). This is the sort of thing of which we need a lot more before we have believable control over statements about what non-supersymmetric vacua of string theory are really up to. Until we have control over these issues, we’ve got to be very careful about what we’re doing in this context, taking explorations of such vacua -and phenomenological conclusions which may be drawn from them- as interesting, but highly tentative. [...]

By: Return to the Fold | Cosmic Variance

Return to the Fold | Cosmic Variance — Fri, 27 Jan 2006 08:06:48 +0000

[...] I always considered it a great loss to the field, over the years, as he is quite a remarkable fellow (he seems to have been lauded at another piano competition again), and several things happened in the field after he left that I always thought that he would enjoy, and moreover bring an interesting and valuable approach to. On the other hand, he was not lost to physics or high energy physics as a whole, and started a series of really creative and singular work in another area, as I’ll mention below. (Ironically, the scope of some of what we did in that last paper we wrote, with Simon Dalley and Anders Watterstam, has only been fully appreciated in some recent work of mine (with Durham Phd. student James Carlisle and USC undergraduate student Jeff Pennington), described in an earlier post. We knew in 1991-2 that we ahd something that would now be called “open-closed duality”, but it is part of an even nicer story, as partially uncovered by Klebanov, Maldacena and Seiberg….. read that post for more, and I should do the next part of that story one day.) [...]

By: Plato

Plato — Mon, 07 Nov 2005 17:42:23 +0000

A general link for the laypeople

By: Clifford

Clifford — Sun, 06 Nov 2005 01:34:58 +0000

Ambitwistor… I’d have to think about that……

-cvj

By: Ambitwistor

Ambitwistor — Sat, 05 Nov 2005 23:15:26 +0000

I think it’s fascinating how an entire string theory can be “hidden” within a simple ordinary differential equation. Are there any examples of field theories arising from ODEs in similarly “non-obvious” ways?

By: Clifford

Clifford — Sat, 05 Nov 2005 21:20:34 +0000

Well, it is much more than that in general……. its most common realisation is in the context of particle physics where it is a symmetry that relates states (e.g. particles) of integer spin (“bosons”) with particles of half integer spin (“fermions”). The first reason this is interesting is because conventional particle physics has a big separation of the roles of these two types of particle…. matter is made of fermions (quarks, electrons, etc) while force is carried by bosons (photons, gluons, etc)… so if Nature once had a phase where it was supersymmetric, then matter and force are united in that phase….. This is but one of the many reasons that supersymmetry is exciting….. Then, as JoAnne has pointed out, the consequences of the relics of supersymmetry can be quite profound, since supersymmetric scenarios predict particles that may show up at the LHC which may be the principal component of Dark Matter……! Supersymmetry may also be tied up with the unification of forces, the origin of mass…so many things…… so it is interesting for lots of reasons…

-cvj

By: Helge

Helge — Sat, 05 Nov 2005 16:05:36 +0000

Well a big thanks again to you Clifford

For everybody else interested. The paper Clifford was refering to, can be found at:
http://www.arxiv.org/abs/hep-th/9405029
Enjoy reading.

My summary of my understanding (which might be wrong) is: Supersymmetry is kinda like added like you add spin. You double the Hilbertspace. However, you also use a modified Hamiltonian.
How you modify it can be found in that paper. (Page 13).

Helge

By: Clifford

Clifford — Sat, 05 Nov 2005 14:32:21 +0000

Helge. Well, later is probably better for this… but the key point is that the potential u for the case of Gamma number of branes and the potential for the case Gamma+1 form a pair of “superpartner” hamiltonians. The transformation between the two is the famous “Backlund” transformation….but there’s a lot more to this….including how to write the whole story so that it has the same algebraic structure as supersymetry algebras in other systems…. where you can discuss supersymmetry breaking, etc…. have a look at the paper. Oh, there is an excellent review by F. Cooper et al, of supersymmtric QM. Search SPIRES for that name and title combination.

cheers,

-cvj

By: Helge

Helge — Sat, 05 Nov 2005 12:09:16 +0000

Hey Clifford
You are asking for it. So what is the supersymmetry transform of that Hamilitonian? Or is there one?
Like for Translations in “time” we would have z -> z + a
Or timereversal z -> -z
And yes I have wondered what supersymmetry is.

Cheers, Helge

By: Plato

Plato — Sat, 05 Nov 2005 03:14:18 +0000

great…..more solitons. I mean…um solutions.

By: Matt B.

Matt B. — Sat, 05 Nov 2005 01:57:30 +0000

Excellent! It’s like elegant universe, but with equations. Thank you.

By: Clifford

Clifford — Sat, 05 Nov 2005 00:01:15 +0000

Hi Helge,

The QM model controls a huge amount of the physics in this case. Once you know what u is (solution of the first equation I wrote…sort of a “master” equation), then you put it in the QM and read off a lot of interesting things…. The spectrum means something in the string theory, the wavefunctions themselves mean something, etc…. and hbar in the QM directly maps to the string coupling in the string theory….so quantum corrections in the usual unergraduate QM sense are the same quantum corrections generated by a topological expansion in a string theory, with all the fancy language you’ve heard about involving sums over Riemann surfaces, etc…. Its all there.

Oh, if you ever wondered what supersymetry was, in essence… that’s there too…the quantum mechanics has a supersymmetric structure!

-cvj

By: Helge

Helge — Fri, 04 Nov 2005 23:49:15 +0000

Hey Michael I am in kinda the same situation as you. Except my next exams are kinda in january, here in Austria. So I get time to look at this stuff right now.

So one more question to Clifford:
Are all these conclusions about closed, open strings etc coming up from that QM-Model?

If yes, it seems a little less magic to me, but even more cooler

And a big thanks to Clifford for answering my questions
Helge

By: Clifford

Clifford — Fri, 04 Nov 2005 23:48:06 +0000

Michael D,

One of the authors of the two papers I mention, Jeff, is an undergraduate. He did not even know much QM when he first started talking with me. He took a book and taught himself what he needed in a short time, and picked up a lot of the other techniques as he went along too. It is a nice combination of string theory and quantum mechanics which showcases the fun stuff you can do with the thigns you learn in undergraduate physics at various levels.

Cheers,

-cvj

By: Michael D

Michael D — Fri, 04 Nov 2005 23:42:49 +0000

Thanks for the post Clifford!

While much of the string theory diagrams/D-branes is above me, as a physics undergrad there are lots of familar terms which encourages me to make sure that I (try) to understand them in my current courses.

Partition function and free energy showed up in 3rd year Thermal, and pertubation theory shows up everywhere from QM, to a maths course i’m taking on Applied Fluid Dynamics (eg. matched asymptotic expansions) as well as in Electrodynamics course with dispersion relations in dielectrics.

What astounds me the most as a I move into higher levels of physics/maths is their reliance on previously learned techniques/knowledge. For example, the non-linear ODE you start with up the top is what you hear about in 1st year “These are complicated, so we won’t do them in thise course.” But in order to solve the higher stuff you of course need to get those basics down.

While it is very tempting to check out the papers as physics ‘study’, best that I look at them after my exams…

Cheers,

By: Clifford

Clifford — Fri, 04 Nov 2005 23:42:05 +0000

Kea… Yes! Yes! We’re on the same page here! Go for it!

-cvj

By: Kea

Kea — Fri, 04 Nov 2005 23:39:07 +0000

Goodness, Clifford. This is so cool! Once one has KdV heirarchies one can get there from SDYM, as in

A self-Dual Yang-Mills Heirarchy and its reductions to Integrable Systems in 1+1 and 2+1 dimensions
M.J. Ablowitz, S. Chakravarty, L.A. Takhtajan
Commun. Math. Phys. 158 (1993) 289-314

or even better, one can do a Twistor correspondence, as in

Twistor correspondences for the soliton hierarchies
L.J. Mason, G.A.J. Sparling
J. Geom. and Phys. 8 (1992) 243-271

I dragged these references out of my filing cabinet after looking at your paper. Must dust them off and read them…..

By: Clifford

Clifford — Fri, 04 Nov 2005 23:37:32 +0000

It is magic to most string theorists…. the few who have noticed that this stuff exists. It should look like magic. It does very clever stuff in a very different way. this makes it important to know about and to learn, but it is not high fashion, so nobody bothers, hardly. But it is well-defined magic, rooted in a number of concrete computations with checks on the construction coming from many places.

I will explain later about u also being a potential in a simple one dimensional quantum mechanics problem, and how the wavefunctions of that problem tell you more about D-branes.

Oh, and maybe I’ll tell how all of this is related to water waves in a canal in ~~Glasgow~~ Edinburgh.

Really.

-cvj

By: Helge

Helge — Fri, 04 Nov 2005 23:29:17 +0000

Hey Clifford First questions are solved I think. I took a look at the paper, and the expression for R looks much more complicated there.
It kinda looks like magic to me right now how you get all that stringy stuff out of the equation. But I completly lack training in string theory …
I skiming through the paper right now. One more thing I just noticed: You use the u as potential (choice of letter is a lot more obvious now).
But sure it sounds all extremly cool.
Cheers,
Helge