How hard is string theory exactly?

[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]

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

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]

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 definitely agree with that description.

I've never understood why people like this book as an introduction.

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 pursue 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 relevant 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 beginning 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!

 

[Kazz]

It's as if we discovered time dilation, but without Einstein ever being born.

 

[negru]

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 pursue the subject.

But this can be an issue with pretty much every single topic in physics. For example just in Classical Mechanics, with dynamical systems and whatnot, there's enough theory to keep anyone occupied for many many years. If you put together all the random research topics, problems or concepts in Classical Mechanics I'm fairly certain the volume will be comparable to all the random research topics and problems in QFT or string theory.

The point is you don't need to know more than 5% of string theory to do research, just like you don't need to know what a symplectic manifold is to do classical mechanics. I guess the difference is that most people can agree what the basics of CM are, but it's not yet clear for ST.

Knowing all string theory is like knowing all of History. Unpractical, unnecessary, most likely impossible.

 

[ImaLooser]

It's as if we discovered time dilation, but without Einstein ever being born.

Huh?

 

[Demystifier]

I agree with negru (and disagree with QGravity).

 

[scottbekerham]

I think (I don't know if it's true) that the most important skill one has to acquire in order to really understand strings is differential geometry and lie groups . Differential geometry is the basic tool to use as one deals with curved surfaces , branes and other geometric structures. Even gauge theory is best expressed using fibre bundles and connections . So you can't get far in string theory without differential geometry .What I want to know is :
Is it sufficient to understand differential geometry from a practical point of view (e.g. nakahara ) or should one learn the foundations of the subject (Which means absolute ragor) (e.g. read spivak textbooks on DG) in order to be able to apply these mathematical ideas in nonconventional and non-trivial way ?

 

[haushofer]

I would say that Nakahara is sometimes already to rigorous. Its treatment on Fibre Bundles and gauge theories is not really a revelation; I've never understood this fetish of some people with fibre bundles anyway.

So imho Nakahara suffices for most applications, unless you really want to do die-hard math. E.g., the proof that certain string theories are anomaly-free is rather involved, and I think that only reading Nakahara doesn't give a thorough understanding. On the other hand, I'm not sure how interesting that is unless you really want to be able to do the full calculation on your own.

 

[sshai45]

About experiment / theory argument, I would say making important experimental discoveries is as hard as making important theoretical discoveries, but the entry barrier is lower. Just look at how many undergrads help out in the labs.

In fact, once you get to the professional level, you're competing with people who have devoted a large part of their life to understanding the subject. It's hard to make truly groundbreaking contribution to any field. So my impression is that when people talk about a subject, e.g. string theory, being hard, what they're really saying is that the entry barrier is high.

So does this mean you can only be ready to compete after spending, say, 25-30 years (a "large part of your life") studying it?

 

[haushofer]

So does this mean you can only be ready to compete after spending, say, 25-30 years (a "large part of your life") studying it?

No, that's impossible. In that time the field already has involved in such a way that you should catch up again, creating some sort of Zeno paradox.

That's why people buy the book of Becker^2 Schwarz. It's horrible as a pedagogic introduction, but it gives a highly compressed overview of the field in less than 1000 pages. It allows people to get the overview which is needed to start research, even though it's more of a "knowing the jargon" than "understanding what's really going on".

One of the hard things about research in theoretisch physics, and string theory in particular, is that you have to find a midway between understanding and being able to contribute to the field. Most people, not being geniuses, will find the following: trying to understand too much does not allow you to contribute, and trying to dive into something very specific doesn't allow you to develop a broad overview and put your findings into the bigger picture. Which can become awkwardly exposed during questions if you give a talk :P