Studying ADS/CFT correspondence at a graduate level

[PhysiSmo]

Hello everyone!

I'm studying string theory at a graduate level and want to focus on ADS/CFT correspondence. The problem is that I don't know where to start from.

I've already learned the bosonic string, some elements of CFT (and BRST quantization), T-duality and how the D-Branes enter the game, some of the D-Branes's properties (like the world-volume action, the coincident D-Branes and the gauge fields that arise etc.) and the way one constructs black holes using D-Branes.

I've also studied QFT at a quite satisfactory level. When it comes to susy, though, I know almost nothing.

What should be the best way to proceed then? I've found 2 reviews that seem pedagogical, namely http://arxiv.org/abs/hep-th/0201253v2" , which contain some basics of susy and supergravity. Should these papers be enough for my purposes, or am I supposed to read something more complete such as the chapters 4,5 of GSW or Becker, Becker and Schwarz?

Moreover, could someone pinpoint me the differences between the world-sheet susy and the spacetime susy? Why can't we have both types in our theories (or do we have so)? When one uses, for example, type IIB superstring theory for ADS/CFT, in which of these two cases do we put the theory?

I'd be really grateful for some help here..

 

[nrqed]

Hello everyone!

I'm studying string theory at a graduate level and want to focus on ADS/CFT correspondence. The problem is that I don't know where to start from.

I've already learned the bosonic string, some elements of CFT (and BRST quantization), T-duality and how the D-Branes enter the game, some of the D-Branes's properties (like the world-volume action, the coincident D-Branes and the gauge fields that arise etc.) and the way one constructs black holes using D-Branes.

I've also studied QFT at a quite satisfactory level. When it comes to susy, though, I know almost nothing.

What should be the best way to proceed then? I've found 2 reviews that seem pedagogical, namely http://arxiv.org/abs/hep-th/0201253v2" , which contain some basics of susy and supergravity. Should these papers be enough for my purposes, or am I supposed to read something more complete such as the chapters 4,5 of GSW or Becker, Becker and Schwarz?

Moreover, could someone pinpoint me the differences between the world-sheet susy and the spacetime susy? Why can't we have both types in our theories (or do we have so)? When one uses, for example, type IIB superstring theory for ADS/CFT, in which of these two cases do we put the theory?

I'd be really grateful for some help here..

Unfortunately I won't be able to answer your questions because I am myself trying to learn that stuff, by myself. But I have some suggestions for background material.

First, the review by Nastase that you cite is excellent, probably the best intro I have seen anywhere. I haven't seen your other reference before but I will look.

As an another pedagogical review of AdS/CFT I would suggest

http://arxiv.org/PS_cache/hep-th/pdf/9902/9902131v2.pdf


And of course there is the huge article

http://lanl.arxiv.org/abs/hep-th/9905111


As for susy, I had never found anything that made any sense to me. I always felt that (at least with my background) too much stuff was thrown at me without justification and without explanations. And the notation was not explained carefully.
Until an excellent introdution by Aitchison was made available:

http://xxx.lanl.gov/abs/hep-ph/0505105

It's only when reading this that I felt that I was starting to feel that I could understand susy and do calculations. Btw, these notes have been expanded into a book which is also excellent.

Do you have any profs at your university available to help answering the questions?
I am a college prof learning that stuff by myself and am unfortunately over one hundred mile away from the closest university where some people could help me (and I doubt they would have the time). It would be nice to have a "study partner".

Unfortunately, there is a slight "anti-string theory" attitude on this board and there are few string theorists hanging around, I think. This is very unfortunate it's such a beautiful theory.

 

[arivero]

Unfortunately, there is a slight "anti-string theory" attitude on this board and there are few string theorists hanging around, I think. This is very unfortunate it's such a beautiful theory.

Actually there are no string theorist hanging in any board, are they? The most you can find is a handful of blogs.

 

[Haelfix]

I can tell you right now, you are more or less on your own. I'm a postdoc at a university and every stringy person (or any other advanced research subject) I know off is more or less self taught (or they go to workshops). Very few universities have classes on the subject and the specialists and their assistants really only have time for a few questions here and there.

Having said that, AdS/CFT is a big enough subject with enough clout that it has by now a large amount of intro papers. I suggest going through the phenomology section first, as the papers will be much more readable and tailored to a wider audience.

 

[BenTheMan]

Unfortunately, there is a slight "anti-string theory" attitude on this board and there are few string theorists hanging around, I think. This is very unfortunate it's such a beautiful theory.

sure there are, you just have to know where to look.

But you are correct...the anti-string bias here is so thick you could cut it with a knife. To be clear, most of the anti-string people here are only interested in talking ABOUT physics, not actually DOING physics. (I know, I've tried---the end result is usually someone cutting and pasting a long list of abstracts (which I can find myself) and telling me that I should read some set of papers which I know I won't understand.) I have to work to not get sick at the constant ``Smolin Book Impact in <month>'' threads, which have nothing to do with Physics.

I agree with Haelfix---you just have to do it yourself. I'd suggest spending a year going through Polchinski and the big yellow CFT book (DiFrancesco).

Also, Samir Mathur is offering a string theory course this quarter. A major focus of his research is doing interesting things with AdS/CFT, so it may be wise to read the notes from his website:
http://www.physics.ohio-state.edu/~mathur/
If you're familiar with bosonic strings/CFTs, then you can probably start with the lecture titled ``Fermions''. There are a number of highlights, including showing that the zeta function relationship $$1+2+\cdots = -\frac{1}{12}$$ graphically.

Moreover, could someone pinpoint me the differences between the world-sheet susy and the spacetime susy? Why can't we have both types in our theories (or do we have so)?

This is a question I have struggled with at times myself. World-sheet SUSY is a symmetry relating the oscillator modes on the world-sheet---that is (in the notation you're likely familiar with) $$\alpha^{\dagger}$$ creates a bosonic harmonic oscillator on the string, and $$b^{\dagger}$$ creates a fermionic harmonic oscillator on the string. There is a mode expansion in terms of fermionic oberators b, just as there is an expansion in terms of $$\alpha$$.

 

[nrqed]

sure there are, you just have to know where to look.

But you are correct...the anti-string bias here is so thick you could cut it with a knife. To be clear, most of the anti-string people here are only interested in talking ABOUT physics, not actually DOING physics.

I would actually say that there is more interest in the sociology of physics (i.e. who is doing what, who is working where, who did his PhD with whom, etc) than even physics. An dyou are right, actually discussions on actually "doing" physics seem rare.

(I know, I've tried---the end result is usually someone cutting and pasting a long list of abstracts (which I can find myself) and telling me that I should read some set of papers which I know I won't understand.) I have to work to not get sick at the constant ``Smolin Book Impact in <month>'' threads, which have nothing to do with Physics.

I agree with Haelfix---you just have to do it yourself. I'd suggest spending a year going through Polchinski and the big yellow CFT book (DiFrancesco).

It's true that people have to learn most of that stuff on their own but is it so much more efficient (not to say enjoyable) to have at least someone to discuss with even if it's someone who is at the same level and not an expert. There are so many little details that one gets stuck on and that can be clarified by talking with someone. Sometimes the other person will point out something obvious we missed, sometimes the answer will become clear just by us formulating a question, sometimes it is reassuring to hear someone else agree that a point is not clear at all, etc.

Also, Samir Mathur is offering a string theory course this quarter. A major focus of his research is doing interesting things with AdS/CFT, so it may be wise to read the notes from his website:
http://www.physics.ohio-state.edu/~mathur/

Excellent reference, Thanks for posting that.


I think we should all use this board to discuss AdS, CFT and string theory. It would be great to get some kind of group interaction going.


Patrick

 

[PhysiSmo]

Good mourning guys, thank you all for your answers!

nrqed, BenTheMan, thanks for the links, I've checked them quickly but they seem nice!

I have to go to my classes, I'll post later further comments and thoughts about all these..

 

[Demystifier]

There are a number of highlights, including showing that the zeta function relationship $$1+2+\cdots = -\frac{1}{12}$$ graphically.

I have not been able to find it. Can you help?

 

[BenTheMan]

I have not been able to find it. Can you help?

See Section 7 here: http://www.physics.ohio-state.edu/~mathur/quantumstring.pdf.

Bottom of pg 8, top of page 9.

 

[arivero]

An dyou are right, actually discussions on actually "doing" physics seem rare.

But it is not forbidden.

 

[PhysiSmo]

I must admit that I'm a little bit worried about the quantity of knowledge one must learn in order to tackle unsolved problems, that is to actually do research in this field. The subject is really vast. I learn one thing only to realize that 10 more doors have been unlocked, and so on...

Do you have any profs at your university available to help answering the questions? I am a college prof learning that stuff by myself and am unfortunately over one hundred mile away from the closest university where some people could help me (and I doubt they would have the time). It would be nice to have a "study partner".

There is only one person who could answer my questions, that is my supervisor! I've already asked him some of these questions, but unfortunately he tends to give total freedom to students when writing a thesis, so that they prepare themselves for standing on their own at the phd level...I wish you the best to continue our efforts on your own!

I knew that it would be something like that, as Haelfix and BenTheMan pointed out, but I expected more guidance, especially in a MSc program..

As for the anti-string bias here, I think that everyone realizes its existence and the problems that arise with such attitudes. I recognize that it's healthy to present different approaches to tackle a huge problem, such as the problem of quantum gravity or the forces unification. It's sad though, to observe total lack of objective behavior here. I too am tired of watching posts ''about'' physics and not about ''doing'' physics..

This is a question I have struggled with at times myself. World-sheet SUSY is a symmetry relating the oscillator modes on the world-sheet---that is (in the notation you're likely familiar with) $$\alpha^{\dagger}$$ creates a bosonic harmonic oscillator on the string, and $$b^{\dagger}$$ creates a fermionic harmonic oscillator on the string. There is a mode expansion in terms of fermionic oberators b, just as there is an expansion in terms of $$\alpha$$.

That said, world-sheet SUSY is nothing more than a string's property. But what about spacetime SUSY? How that symmetry manifests? Are the various superstring theories theories with world-sheet AND spacetime SUSY? Are there explicit actions for these theories?

But it is not forbidden.

How could something like that be forbidden? I thought this was a physics forum, not a salesrank and statistics presentation!

 

[nrqed]

I must admit that I'm a little bit worried about the quantity of knowledge one must learn in order to tackle unsolved problems, that is to actually do research in this field. The subject is really vast. I learn one thing only to realize that 10 more doors have been unlocked, and so on...

That's very true. Ome must have a very good grasp of QFT, GR, CFT, differential geometry, etc.

There is only one person who could answer my questions, that is my supervisor! I've already asked him some of these questions, but unfortunately he tends to give total freedom to students when writing a thesis, so that they prepare themselves for standing on their own at the phd level...I wish you the best to continue our efforts on your own!

I knew that it would be something like that, as Haelfix and BenTheMan pointed out, but I expected more guidance, especially in a MSc program..

Well, yes, one would expect your advisor to offer much more guidance, especially at the MSc level. There is so much to learn, one needs guidance to know what to focus on and to get helped when one gets stuck.

As for the anti-string bias here, I think that everyone realizes its existence and the problems that arise with such attitudes. I recognize that it's healthy to present different approaches to tackle a huge problem, such as the problem of quantum gravity or the forces unification. It's sad though, to observe total lack of objective behavior here. I too am tired of watching posts ''about'' physics and not about ''doing'' physics..

I thought I was the only one...

Yes, I wish that the focus was on just learning the physics of all the exciting stuff such as string theory, loop quantum gravity, noncommutative geometry, and so on, without any of the usual criticisms about string theory or whatever. Now and then there is a serious physics question which is usally left unanswered because tehre are few people around actually working on the physics. But posts about "sociology" lead to many replies.

That said, world-sheet SUSY is nothing more than a string's property. But what about spacetime SUSY? How that symmetry manifests? Are the various superstring theories theories with world-sheet AND spacetime SUSY? Are there explicit actions for these theories?

Do you have GSW? It's old but still an excellent book to learn the basic ideas. Theer are good discussions on that point there.

 

[BenTheMan]

I knew that it would be something like that, as Haelfix and BenTheMan pointed out, but I expected more guidance, especially in a MSc program..

I had a similar experience with my MS advisor. The best advice I can give you is to find some graduate students that are also interested, and have biweekly meetings. You can't go wrong with GSW and Polchinski, and a myriad of lecture notes that are free on the web. Also, Peskin's TASI lectures from like 1992 are pretty good: http://www.slac.stanford.edu/spires/find/hep/www?rawcmd=FIND+A+PESKIN+AND+K+CONFORMAL+and+k+introduction&FORMAT=www&SEQUENCE=

 

[PhysiSmo]

I had a similar experience with my MS advisor. The best advice I can give you is to find some graduate students that are also interested, and have biweekly meetings.

Yes, that's a very good idea, I intended to do so..

You can't go wrong with GSW and Polchinski, and a myriad of lecture notes that are free on the web. Also, Peskin's TASI lectures from like 1992 are pretty good: http://www.slac.stanford.edu/spires/find/hep/www?rawcmd=FIND+A+PESKIN+AND+K+CONFORMAL+and+k+introduction&FORMAT=www&SEQUENCE=

Thanx for the link, I hadn't found Peskin myself. I think I'll begin with GSW, I really enjoyed the first 3 chapters.

Thank you all for your comments, it's good to feel you're not alone, or that other people experience similar problems with yours and surmount them, it's kind of relaxing and relieving!

 

[geoffc]

I found the following video links useful:

Pacific Institute of Mathematical Sciences has three intro lectures:
http://www.pims.math.ca/science/2003/fmp/

 

[lbrits]

I must admit that I'm a little bit worried about the quantity of knowledge one must learn in order to tackle unsolved problems, that is to actually do research in this field. The subject is really vast. I learn one thing only to realize that 10 more doors have been unlocked, and so on...

Yes, and this feeling won't go away for a number of years. I'd highly recommend you get a copy of Clifford Johnson's book on D-branes (or, his notes, which are based on Polchinksi's lectures). The book is a fleshed out version of those notes. For a weekend's reading, I would also recommend Szabo's book.

 

[PhysiSmo]

Yes, and this feeling won't go away for a number of years. I'd highly recommend you get a copy of Clifford Johnson's book on D-branes (or, his notes, which are based on Polchinksi's lectures). The book is a fleshed out version of those notes. For a weekend's reading, I would also recommend Szabo's book.

Actually Johnson's book is my main textbook for the subject I've read chapters 1,2,4,5,10,11, most of chap. 17 and tried to read 18 but realized enormous knowledge cavities to proceed.

I returned, then, and read chapter 3 and some elements of chap. 7. But Clifford assumes prior knowledge of susy, thus my initial brainstorming..

 

[lbrits]

Sorry, I misread your initial post a bit.

Worldsheet susy comes about when you want spacetime fermions. E.g., first-quantizing a relativistic point particle, you will need worldline spinors and you'll obtain worldline susy. However, this doesn't have spacetime susy.

For the RNS string, worldsheet susy comes about manifestly, whereas spacetime susy is a property of interactions and the spectrum, and is related to GSO and modular invariance.

And in some cases, spacetime susy is broken (usually by presence of D-branes or other boundary conditions).

For the purposes of doing AdS/CFT, a lot of susy reviews might be overkill, as they are related to phenomenology and QFTs, and the subject is quite vast as you've discovered. Have you looked at GSW and Polchinski on this regard?

 

[nrqed]

Sorry, I misread your initial post a bit.

Worldsheet susy comes about when you want spacetime fermions. E.g., first-quantizing a relativistic point particle, you will need worldline spinors and you'll obtain worldline susy. However, this doesn't have spacetime susy.

For the RNS string, worldsheet susy comes about manifestly, whereas spacetime susy is a property of interactions and the spectrum, and is related to GSO and modular invariance.

And in some cases, spacetime susy is broken (usually by presence of D-branes or other boundary conditions).

For the purposes of doing AdS/CFT, a lot of susy reviews might be overkill, as they are related to phenomenology and QFTs, and the subject is quite vast as you've discovered. Have you looked at GSW and Polchinski on this regard?

the amazing thing is that after GSO projection, some of the worldsheet fermions states correspond to bosonic spacetime states! And some states correspodn to spacetime fermions. I am still trying to understand how this works. This was surprising to me.

 

[nrqed]

Actually Johnson's book is my main textbook for the subject I've read chapters 1,2,4,5,10,11, most of chap. 17 and tried to read 18 but realized enormous knowledge cavities to proceed.

I returned, then, and read chapter 3 and some elements of chap. 7. But Clifford assumes prior knowledge of susy, thus my initial brainstorming..

I'd like to know how you find that book? I was not sure if it would be over my head. Can you learn from it?


I'd like to recommend a book that I find incredibly interesting and useful. Surprisingly I have never heard it mentioned in forums. I found it by luck while browsing on amazon. It is "Gravity and Strings" by Tomas Ortin. It is packed with information. At 650 pages long (and almost one thousand references) it is incredible in its coverage. But the best is that it is fairly pedagogical. I can actually follow most of what is written so I am learning a lot from it. AdS/CFT is not treated but a lot of the background information required to understand the conjecture is covered.

 

[PhysiSmo]

Sorry, I misread your initial post a bit.

Worldsheet susy comes about when you want spacetime fermions. E.g., first-quantizing a relativistic point particle, you will need worldline spinors and you'll obtain worldline susy. However, this doesn't have spacetime susy.

For the RNS string, worldsheet susy comes about manifestly, whereas spacetime susy is a property of interactions and the spectrum, and is related to GSO and modular invariance.

And in some cases, spacetime susy is broken (usually by presence of D-branes or other boundary conditions).

For the purposes of doing AdS/CFT, a lot of susy reviews might be overkill, as they are related to phenomenology and QFTs, and the subject is quite vast as you've discovered. Have you looked at GSW and Polchinski on this regard?

Thank you for your answer!

Yes, the most susy reviews are overkill, indeed. I decided to start with GSW and continue with AdS/CFT reviews later..

I'd like to know how you find that book? I was not sure if it would be over my head. Can you learn from it?

Yes, you can learn from it! It's not very difficult, it's perhaps less rigorous than Polchinski or GSW, trying to be more pedagogical and intuitive.

It's a great book, although it mostly focuses on D-Branes. There are better books though to learn string theory basics, for sure. For example, I found GSW much more intuitive and pedagogical, and of course more analytic than Clifford (the bosonic string is about 70p in Clifford and 130 in GSW!).

On the other hand, it's the only book (as far as I know) that treats D-Branes so extensively, which have become fundamental ingredients in the theory. In that sense, it's a valuable resource for the subject.

 

[Demystifier]

See Section 7 here: http://www.physics.ohio-state.edu/~mathur/quantumstring.pdf.

Bottom of pg 8, top of page 9.

Thanks!

 

[dipstik]

Author West, P. C. (Peter C.)
Title Introduction to supersymmetry and supergravity / P. West.
Publication Information Singapore ; Philadelphia : World Scientific, c1986.

... spent most of the time in the appendix.

 

[lbrits]

Author West, P. C. (Peter C.)
Title Introduction to supersymmetry and supergravity / P. West.
Publication Information Singapore ; Philadelphia : World Scientific, c1986.

... spent most of the time in the appendix.

This might be good also: http://arxiv.org/abs/hep-th/9805055

 

[BenTheMan]

When studying supersymmetry, the question is...what do you want out of it?

If you only want enough SUSY to do string theory, I can't argue with the reccomendation of West's book...most of the ``hardcore'' string theorists I know love it.

I'm more of a ``softcore'' string theorist---if you are interested more in particle physics and phenomenology, you should check out (in this order) Binetruy's book, Terning's book/lecture notes, and then Dine's book, always using Bagger and Wess (which is terrible to learn from but a great reference because everyone uses his notation---it's basically just a list of formulae). Binetruy's is a great place to start, and you should be very familiar with about the first 5-7 chapters. Dine's book has potential, and I would wait for an expanded second edition, though. I'm at least holding out hope. For a good intro into the phenomenology, read Steve Martin's ``Supersymmetry Primer'', which is on the arxiv.