How hard is string theory exactly?

dkotschessaa

Is string theory still as "hot" in Academia as the popular books and TV documentaries (Such as the Elegant Universe) make it out to be? The Elegant Universe (Nova special) all but suggested that practically everybody who was going to school for physics was studying string theory. Really? Brian Greene comes across as something of a sham-wow salesman in that documentary and makes it hard for me to take him seriously.

-DaveKA

dkotschessaa

Oh and of course you can buy "String Theory for Dummies" at Amazon now.

(He says cynically as he secretly plans to buy it in the near future)

-DaveKA

humanino

Brian Greene is certainly too enthusiastic for my personal taste. In my opinion, there are better popular accounts, such as Randall's. This being said, we should keep our minds open. String theory is still the most active and fruitful merely in terms of number of articles written, which simply reflects a number of researchers. Just have a look on arXiv for yourself.

IMHO, one of the reasons M-theory is so difficult is that it is a non-perturbative problem.

How is that helpful ? Say, if you take Zee's last edition, you fill find clearly that one mainstream point of view is that it does not matter so much whether SUSY is realized in Nature or not. There are many papers which are not concerned by this question. People study N=4 YM because it is a playground in which we may be able to get insights and improve our handling of even scalar fields.

Demystifier

QCD at low energies is also a non-perturbative problem, but it is much less difficult than M-theory because we still have a well-defined QCD action, so we know what exactly IS the problem. The problem with M-theory is that we don't even know what exactly is the problem.

My point is the following. It is usually simpler to solve a theory with more symmetry. For example, QCD with a chiral symmetry (with all masses put to zero) is simpler than true QCD. Unbroken SUSY is another example. However, it is at best questionable how much such oversimplified theories really help to understand the true stuff.

Demystifier

There is also a big difference between first and second superstring revolution.

After the first revolution, physicists were able say: Good, now we understand the theory much better.

But after the second revolution, they could rather say: Now we see that there is much more to understand than meets the eye.

Kracatoan

String "Theory" is a complex topic, made more complex by that fact that is is more of a pseudo-science than proper physics - It can't be tested and doesn't make any unique predictions. Rather than try to understand string theory right now, stand back, and see if anything is actually achieved by it. Only then will it be worth the bother investigating it.

I reccomend reading Lee Smolin's "The Trouble with Physics" for a more detailed critical analysis of string theory.

crackjack

There is enough room (by way of hitherto-unused, modern geometrical tools, in addition to undiscovered physics itself) in string theory to do it as "hard" as you would like to do it. While some might find generating creative physical principles hard, others find understanding and applying math tools to be hard.

humanino

And do YOU claim to really have studied and understood string theory, or do you simply repeat what Smolin said ?

Kracatoan

No. Naturally I've spent most of my time as a Physicist reading as much around the topic as I can, and seeing as String Theory is the in thing at the moment, I've read extensively on the topic. It was just that reading Smolin's book provided a refreshing view of string theory, not as a theory which is currently favoured, but instead as a mathematical curiosity, a view which has been mirrored by pretty much everyone I've talked to at Cambridge and Imperial. However, not everything Smolin says is sensible and and I do disagree with him on many counts, such as DSR, but thats that.

humanino

Well, thank you for your honesty and perspective. Since you mention UK institutions, I would be interested to hear the update of Penrose's opinion on string theory. There has been tremendous attention paid to the twistor formalism ever since Witten's 2003 article. This approach is essentially a revival of S-matrix method. It has provided very concrete calculation for QCD backgrounds at the LHC, and this is independent of whether string theory is realized at a fundamental level. Simply, playing with string theory (say as a toy model if you want), we discovered new methods to go beyond Feynman's perturbative calculations.

I imagine you have also heard of high-T superconductors. Another example where string theory provides calculations, which makes it interesting and achieving important results, while not proving to be "fundamental" in the "popular" sense.

Kracatoan

That approach, to me, does seem to be the right one. Not accepting the theory completely, but instead using its mathematics, techniques and essentials to further our current model.

marcus

That point of view appeals as highly reasonable. I can see string mathematics being applied usefully in various directions, at various scales, even if not providing a fundamental unifying theory.

It is also possible that interesting math will grow out of LQG. See for example:
http://arxiv.org/abs/1010.1939
Feynman rules for 2-complexes (spinfoams)
Group field theory techniques (including the idea of a graph Hilbert space)
Spin networks (an earlier idea of Penrose but developed in this context)

Also the general idea of a quantum theoretical presentation of geometry, and of constructing quantum field theory not on a pre-established classical spacetime geometry but on the corresponding quantum geometry---the mathematical gains from addressing this problem (while not so widely recognized) could also be significant.

elfboy

it is unimaginably difficult...to put it succinctly

scottbekerham

It's very difficult due to the huge amount of knowledge you have to master in order to make any interesting contribution to the field and the physics is also inherently very difficult so it's difficult on both physics and math side. However , If you want to know what's string theory is all about . You can pick the book "string theory demystified " or a somewhat more advanced book " String theory and M theory" ,You can understand things in those books which gives an impression that it's not difficult at all

haushofer

That's not really strange. A lot of stuff is not explained in these books. Especially "String theory and M theory" by Becker^2 and Schwarz, which after some chapters is more like an encyclopedic overview than a pedagogic explanation. I've never understood why people like this book as an introduction.

Demystifier

I definitely agree with that description.

Neither did I, but several possible explanations come to my mind:
- Because they are much more CLEVER than me and you.
- Because they want to LOOK much more clever than they really are.
- Because by "introduction" they actually MEAN "encyclopedic overview".

By the way, as a more advanced textbook on string theory I like:
M. Kaku, Introduction to Superstrings and M-theory
But for some reason, mainstream string theorists don't like this book at all.

QGravity

in my opinion String Theory is really a hard subject (either considering it physically sensible or just a mathematical curiosity) because the amount of material one must know to learn and persue the subject. just look at the contents of the "Quantum Fields and Strings - a Course for Mathematicians". if you want to learn the subject, my suggestions are as follows:

1) you must master (really doesn't mean that you must know everything, just the basics) the QFT especially the path integral and BRST methods for quantization of gauge theories; for this see Zee's "Quantum Field theory in a Nutshell" or Srednicki's "Quantum Field Theory" (for path integrals, Srednicki's book treated BRST also) and "Aspects of BRST Quantization" or "Quantization of Gauge Systems" (for BRST Methods);
2) you must master in 2-D conformal field theory, for this the first 6 chapters of Di francesco et al "Conformal Field Theory" is sufficient;
3) you must master General Relativity, for this see Schutz "A First Course in General Relativity" or Hartels's "Gravity : an Introduction to Einstein's General Relativity";
4) the relevent mathematics (just for start) is topology, differential geometry, complex geometry, some algebraic topology; the relevant parts of Nakahara's "Topology, Geometry and Physics" are excellent. acquaintance with group theory and representation of groups is mandatory. familiarity with differential and complex geometry of Riemann Surfaces is helpful.

for Books I recommend the followings:
1) "a First Course in String Theory" by B.Zwibach (there is no need for the above mentioned prerequisite); in my opinion a "must read" to know the basics! Excellent at pedagogical style!
2) "Lectures on String Theory" or its update "Basic Concepts of String Theory" by D.Lust & S.Theisen & R.Blumenhagen(required CFT is thoroughly explained); an excellent book to start with; without exercise
4) "The Superstring Theory" by three authorities of the field M.Green, J.Schwarz and Ed.Witten; its start with dual resonance models which is not treated in any other books. in my opinion "required reading" despite of 25 years has been passed sice its publication. mathematical parts, written by Ed.Witten, are excellent; a great second book; without exercise;
3) "Introduction to Strings and Branes" by P.West, a new book with nice presentation of spinors and the role of lie algebras in string theory; a good second book; without exercise
4) "String theory in a Nutshel" by E.Kritsis, a good second book with exercise!
5) "String theory and M-theory : an Introduction" by K&M Becker and J.Schwarz, as our friends stated this book is encyclopedic in some parts and need to be suppelmented by another math or physics book, a good second book with exercises;
6) "Vol.01 - Bosonic String Theory" and "Vol.02 - Superstring Theory & Beyond" by J.Polchinski, a very nice but at the same time hard book which in my opinion in "required reading". Polchinski is a master of QFT and String theory and founder of D-Branes, and its insights are very helpful, a good second or third book with good exercises!
7) "D-Branes" by C.Johanson: a good book on advanced topics such as Quiver gauge theories, Holographic Renormalization group and etc, a third or forth reading without exercise
8) "Gravity & Strings" by T.Ortín; an advanced text that assumes you know string theory, very good on "the stringy gravity"

the two good critical books on String theory are:
1) "The Trouble with Physics" by L.Smolin;
2) "Not Even Wrong" by P.Woit

if you want to know just the basics, I think that "Superstringtheory.com" and Wikipedia Articles or just Zwibach's book are sufficient! the following books are also very valuable:

1) "The Birth of String Theory" by A.Cappelli
2) "D-Brane: Superstrings and New Perspective of Our World" by K.Hashimoto

you must know that these are just the begining and more advanced topics such as Topological String Theory and the ones treated on the "Quantum Fields and Strings - a Course for Mathematicians", or mathematically oriented topics which are related to Field Theory and String Theory such as String topology, Quantum Cohomology and Gromov - Witten Theory and etc are much more subtle and complex!
all in all, String Theory is a fascinating subject that worth learning. I always wonder why when one goes from 0-D particles to 1-D strings gets such a tremendous amount of new mathematics and theoretical (not necessarily physical!) ideas!
Good Luck!