The best books on String Theory

What is string theory?

String theory is an attempt to describe all particles and all forces in nature in one unified theoretical framework. It encompasses quantum mechanics and gravity, and it is based on the idea that the fundamental building blocks of matter are not particles, but strings: objects which have some length, and which can vibrate in different ways.

The first book you’ve chosen is Superstring Theory, Vols 1 and 2. This is pretty technical, isn’t it? 

As a practitioner of the subject I am drawn to the serious accounts. The two volumes by Green, Schwarz and Witten are a wonderful early account of the subject. It was a subject that first fluoresced in the mid-80s. The notion of string theory was already present, even in the late 1960s, but only in 1984, with the work of Green and Schwarz, did people realise string theory could really be consistent with quantum mechanics, as well as including gravity, and could provide theories that looked very much like the standard model of particles. So there was this tremendous light-bulb moment, where everybody said, ‘Oh my God! This could work.’ And that book, Superstring Theory, captures that era in a very substantive way – as well as being a fairly readable account. In terms of readability, I would say even non-physicists could get something out of the first chapter, and then later chapters, they’re more for practitioners.

Yes, my nephew, who did a masters degree in physics, didn’t recommend it as one to dive into. He said in a semester-long undergraduate course they only got halfway through the first volume…

Yes, there’s a lot there. What’s amazing is that all this came together in such a hurry – a lot of the material in that book is the result of two-and-a half years’ activity. There was an incredible upwelling of creativity in that era and these two books are the record of it.

It isn’t out of date just because it dates a while back now? It must be a quickly evolving field.

It’s true. John Schwarz once remarked to me that the things he most regrets having left out of that pair of books were the developments that happened shortly after they published it. But that indicated that it was indeed part of a quickly evolving field, and captured what was going on in a really compelling way. It really hastened the development of the field for a while. There must be parallels in other fields, where you have some solid contribution that really pushes the field forward in a remarkable way…

You told me you put your books in order, does this mean this is your favourite?

Yes. There is something unusual and special about Green, Schwarz, Witten. It was a book very much of the moment, and yet a classic – the words instant classic spring to mind. If we compare it, for example, to Polchinski’s book, another great account – in fact the one that I have used myself the most…

Yes, what about going on to the Polchinski book, String Theory, Vols 1 and 2?

Polchinki’s book stands as a very different achievement. It’s something which he spent years writing and refining, so it’s this gorgeously edited and refined book. He also retains an impressive website where he’s caught all the errors in the equations, and corrected them. It is a work of tremendous care and detail, but it doesn’t quite have that quality of Green, Schwarz, Witten of being the instant classic. It’s more the considered classic.

Tell me more about why it’s significant.

It includes the key early ideas of what’s known as the second superstring revolution. People had taken the notions from the Green, Schwarz, Witten textbook (and the many papers on which it was based) as far as they were going to go, and it seemed that some really new ideas were needed. Those ideas had a more geometrical flavour. They had to do with dimensions of space and time emerging from dynamics, and with new objects, other than strings, entered into the story. And that is where Polchinski made his own greatest contribution, which goes by name of the D-brane. D-branes are a big part of my own book on string theory, and they are objects like strings in that they have spatial extent; but they’re much heavier than strings. These are some of the ideas that Polchinski brought into the field, through his research papers, and he captured those ideas in his book in an elegant and very systematic way.

On the subject of elegance, what about your next choice, The Elegant Universe?

This is a really popular account, probably more in line with what you were expecting. Brian Greene is a distinguished researcher, and he was the first to make an all-out effort to really connect to the public with the main ideas of modern string theory. Others, like Kaku, had made admirable earlier efforts, but Greene really got it off the ground, saying we can tell the public what the string theory is all about, right now. And he did a great job. The book works at many levels – I gave a copy to my mom when it came out, and I also received very positive impressions about the book from Norman Ramsey, who is a Nobel Prize physicist at Harvard. So it’s a great achievement, and part of why it’s a great achievement is that it covers not only string theory but also the accepted pillars of 20th-century theoretical physics, namely, quantum mechanics and relativity. He spends half the book going through these accepted theories in a way that is really approachable to the lay person. So two thumbs up.

Someone who doesn’t come from a science background can read this book and feel they understand what happened in the 20th century physics-wise?

I think that’s right. If you’re looking at the broad sweep of the fundamental theories of physics and particularly string theory, The Elegant Universe is definitely a good pick, though not the only good pick.

Your next book, A First Course in String Theory, is more for students, presumably?

Yes. This is a book by my MIT colleague Barton Zwiebach, and it grew out of a year-long course that he taught at MIT for undergraduates who wanted to learn string theory. So he goes through a lot of the material that the Green, Schwarz, Witten and Polchinski books cover at a more detailed level. He does it without any claims of completeness, but you really do get the idea. I remember when I learned string theory myself, the thing that was hard was that you seemed to have to learn every idea three or four times over, because everything had been thrashed out with different methods, by different groups, in competition with one another, and to get the whole picture you had to absorb so much. Zwiebach’s achievement here is that he found a pretty short and direct path through the centre of the subject that really makes it more accessible.

So the audience you are targeting here is undergraduate physics majors. 

I think that’s fair. Or at least students with a strong science background and good knowledge of calculus. For instance, one of his chapters is ‘A Brief Review of Lagrangian Mechanics’, which is a very challenging topic, having to do with multi-variable calculus. So you definitely have to be on your toes to get the full substance of parts of Zwiebach’s book. But of all the books I’ve mentioned, this one is the most direct route into the heart of the subject.

Lastly, we’ve got the Lectures on String Theory by D Lust and S Theisen.

This is the book by Dieter Lust and Stefan Theisen, which I included partly for sentimental reasons because it is, in fact, the book from which I learned string theory. But it’s also a great book. Among its advantages is that it has good, straightforward prose descriptions of what is going on. It does layer on the algebra that you need in order to really get the subject. But it seemed to me at the time that it was better than other books at telling you upfront, ‘Here is what we’re going to do – and here’s why.’ So it was a very good pedagogical book on the subject. It shares some of the same positive qualities as Zwiebach’s book, but it’s shorter. This is something that I value greatly, because nobody really gets through 300 pages of physics. Not even most professors really pick up a 300-page book or paper and read it. If you really want to be understood, brevity is a good thing.

This book is aiming at what level of knowledge?

I would say advanced undergraduates and beginning graduate students. It’s comparable to Zwiebach’s book. Zwiebach’s book is easier to get started on, but hard to finish, because there really is a lot there. In Lust and Theisen, first of all it is string theory of an earlier era, when things were simpler, and there wasn’t quite so much to learn. But they really do get to the heart of the matter of how string theory might be a so-called ‘theory of everything’.

Which is?

A theory that encompasses all forces of nature and includes all the fundamental particles that we see. That doesn’t mean it’s a theory that will allow you to calculate everything. That would be truly a wonderful theory to have, but string theory is not likely to provide that any time soon. Its aim is much more modest – it’s to provide the umbrella under which all fundamental interactions fall.

There would still be at least as much scope for condensed matter physics, whose aim is not to discover any fundamental interactions, but instead to describe how objects interact when there aren’t very many of them. You have this broad tapestry, with string theory on one side, trying to get at the most reductive and simple fundamental features, and there are other parts, like condensed matter physics, which are all about what happens when you get more things into your system than you can keep track of one by one.

One problem with string theory that I’ve heard is that there is not just one string theory, there are a number that coexist, rendering the predictive power of string theory, its ability to explain physical phenomena, void. Is that a valid criticism?

Yes and no. It’s certainly oft-repeated. One quick comeback would be to say quantum field theory is like that too, but nobody complains about it. This is the theory that Richard Feynman won his Nobel Prize for, where you are describing the quantum mechanics of relativistic particles. And if you just start with that as your goal you get a wonderfully broad and inclusive structure, which can deal with all sorts of things – it can deal with electrons, protons, neutrons and so on and so forth. But by itself, it only has so much information and you have to supplement quantum field theory with a lot of specific knowledge of physics before you’re going to get anything out of it. The quick comeback would be to say, it’s always like that – whenever you have a theoretical framework it has always been the case that you have to include facts about the world. It’s true that historically, in the 1980s, people did suggest the idea that string theory might be different. That maybe in string theory, you wouldn’t have to add in facts about the world before you could get something out of the theory; you could just sit down and calculate everything. I never said that. I wasn’t working in string theory at the time. I wouldn’t have expected it, and it didn’t happen, but what else is new? It’s true of all theories that we know – so string theory is no better and no worse in that regard.

Where I really do worry is the extent to which string theory can be connected to modern experiment. It’s one thing to say that you have to put in facts about the world before you can get anything out, but a far greater worry is, once you put in facts about the world, what do you get? So what I’m working on right now is that very question. What can you get out about modern physics, once you are willing to use string theory as a calculational tool rather than saying it’s going to be just a theory which predicts everything from scratch? Instead you say, I’m going to use this set of ideas to understand experiments. In fact there have been a number of calculations in the past five to seven years, where some strikingly successful numerical predictions have come out of string theory.

Yes, I was going to ask, will string theory lead to testable predictions this century?

To an extent, the calculations that people have done related to heavy ion physics are in that category. The trouble is that heavy ion collisions are complicated affairs. They’re like an enormous car crash where everything breaks, there’s tremendous confusion, and then you try to sort out afterwards what happened. So any kind of numerical description of it is inevitably going to have some uncertainties, and the degree to which string theory calculations work I would say is a factor of two. String theory might predict that such and such number is one, and the experiment might say well it’s about two, but it could instead be one. That’s the kind of accuracy with which things can typically be done.

Now there are some things that are measured, and there is some hope that string theory calculations get them right within 15 to 20 per cent. But I think that’s asking a lot of both the experimental and the theoretical work. There are yet other calculations, say in quantum field theory, where the numbers are known to seven, ten decimal places, both in theory and in experiment – and they work. That’s a bar string theory is not going to clear any time soon. It might get there this century – maybe. I think we’d have to learn a lot more about string theory as a theory, and a lot more about what’s going on at the LHC [Large Hadron Collider in Geneva]. But if 15 years ago you had suggested to me that we’re going to explain some of the aspects of heavy ion collisions that we’ve been working on in the past few years, I would have been very surprised. So no one knows the future.

What’s your view on the LHC. Do you think the first evidence for supersymmetry will come out of the upcoming experiments?

That would be wonderful. I devoted an entire chapter of my book to supersymmetry and the LHC because it’s the great white hope of many theorists that the LHC will discover exactly that. Supersymmetry would be a new way of understanding space and time, and it’s closely tied to string theory – the two ideas grew up together and string theory clearly implies supersymmetry at some level, so to imagine supersymmetry without string theory would be unnatural. And supersymmetry may be experimentally within reach of the LHC.

So that would be a big, big deal. Of course it might happen and it might not. One of the reasons I like to talk about some of the recent successes applying string theory to other kinds of collisions – not the LHC collisions, but the heavy ion collisions – is because there I can point out calculations in string theory where they already have been done, and we can already approximately agree that they work. So, come what may, we can point to this stuff and say, ‘String theory did this.’ There is something here to build upon.

So even if things don’t work out in Geneva… When will we know, by the way?

I wish I could tell you. Positive evidence would be far more compelling than negative evidence. If they discover a whole bunch of new particles and they approximately fit the pattern that supersymmetry predicts, then a lot of people will say, ‘It’s time for the champagne.’ And it would be time for the champagne, even though it would take a lot more than new particles to be sure supersymmetry is right. If they don’t see such particles, then, unfortunately, we would still be left in doubt, because what could happen is that supersymmetry can be part of some theories, but it can predict particles that are a little too heavy for the LHC to produce in any quantity. If that’s the case, it’s bad luck that the LHC is almost powerful enough, but not quite powerful enough, to see supersymmetry.

I myself would prefer the outcome that the LHC discovers something totally unexpected. And then we would all race around and try to figure out what is actually going on, and no doubt use string theory, among other tools, to try and understand it.

It’s impossible to predict what will happen.

If we knew what would happen, there wouldn’t be any point spending the billions of dollars to build the LHC. Supersymmetry is the most likely outcome of the LHC, but only in the sense that it’s more likely than any other comparably specific outcome you can name. I’m not saying it’s particularly likely – I don’t know. There are other possible outcomes: for example, the LHC might produce microscopic black holes. I really don’t think that’s likely. It would take a series of coincidences that seems to be off the wall. Possible, but off the wall.