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T h e L i ttl e B o o k o f S t r i n g T h e o r y

Books in the SCIENCE ESSENTIALS series bring cutting-edge science to a
general audience. The series provides the foundation for a better understanding
of the scientific and technical advances changing our world. In each volume,
a prominent scientist—chosen by an advisory board of National Academy
of Science members—conveys in clear prose the fundamental knowledge
underlying a rapidly evolving field of scientific endeavor.
The Great Brain Debate: Nature or Nurture,
by John Dowling
Memory: The Key to Consciousness,
by Richard F. Thompson and Stephen Madigan
The Faces of Terrorism: Social and Psychological Dimensions,
by Neil J. Smelser
The Mystery of the Missing Antimatter,
by Helen R. Quinn and Yossi Nir
The Long Thaw: How Humans Are Changing the
Next 100,000 Years of Earth’s Climate,
by David Archer
The Medea Hypothesis: Is Life on Earth Ultimately Self-Destructive?
by Peter Ward
How to Find a Habitable Planet,
by James Kasting
The Little Book of String Theory,
by Steven S. Gubser

the
L i t t l e B o o k
of
S t r i n g T h e o ry
St e v e n S. Gu bse r
pr inceton univ ersity pr ess pr inceton and ox for d

Copyright 2010 © by Steven S. Gubser
Requests for permission to reproduce material from this work
should be sent to Permissions, Princeton University Press
Published by Princeton University Press,
41 William Street, Princeton, New Jersey 08540
In the United Kingdom: Princeton University Press,
6 Oxford Street, Woodstock, Oxfordshire OX20 1TW
All Rights Reserved
Library of Congress Cataloging-in-Publication Data
Gubser, Steven Scott, 1972-
The little book of string theory / Steven S. Gubser.
p. cm. — (Science essentials)
Includes index.
ISBN 978-0-691-14289-0 (cloth : alk. paper)
1. String models—Popular works. I. Title.
QC794.6.S85G83 2010
539.7'258—dc22
2009022871
British Library Cataloging-in-Publication Data is available
This book has been composed in Bembo
Printed on acid-free paper. ∞
press.princeton.edu
Printed in the United States of America
10 9 8 7 6 5 4 3 2 1

C o n t e n ts
Introduction 1
C h apt e r o n e Energy 11
C h apt e r tw o Quantum Mechanics 19
C h apt e r t h r e e Gravity and Black Holes 34
C h apt e r f o u r String Theory 49
C h apt e r f i v e Branes 69
C h apt e r s i x String Dualities 99
C h apt e r s e v e n Supersymmetry and the LHC 117
C h apt e r e i g h t Heavy Ions and the Fifth Dimension 140
Epilogue 159
Index 163

This page intentionally left blank

I n t r o duct i o n
String theory is a mystery. It’s supposed to be the the-
ory of everything. But it hasn’t been verified experimen-
tally. And it’s so esoteric. It’s all about extra dimensions,
quantum fluctuations, and black holes. How can that be the
world? Why can’t everything be simpler?
String theory is a mystery. Its practitioners (of which I am
one) admit they don’t understand the theory. But calculation
after calculation yields unexpectedly beautiful, connected
results. One gets a sense of inevitability from studying string
theory. How can this not be the world? How can such deep
truths fail to connect to reality?
String theory is a mystery. It draws many talented gradu-
ate students away from other fascinating topics, like super-
conductivity, that already have industrial applications. It
attracts media attention like few other fields in science. And
it has vociferous detractors who deplore the spread of its
influence and dismiss its achievements as unrelated to em-
pirical science.
Briefly, the claim of string theory is that the fundamental
objects that make up all matter are not particles, but strings.
Strings are like little rubber bands, but very thin and very
strong. An electron is supposed to be actually a string, vibrat-
ing and rotating on a length scale too small for us to probe
even with the most advanced particle accelerators to date. In

2
i n t r o duct i o n
some versions of string theory, an electron is a closed loop of
string. In others, it is a segment of string, with two endpoints.
Let’s take a brief tour of the historical development of
string theory.
String theory is sometimes described as a theory that was
invented backwards. Backwards means that people had pieces
of it quite well worked out without understanding the deep
meaning of their results. First, in 1968, came a beautiful for-
mula describing how strings bounce off one another. The
formula was proposed before anyone realized that strings had
anything to do with it. Math is funny that way. Formulas can
sometimes be manipulated, checked, and extended without
being deeply understood. Deep understanding did follow in
this case, though, including the insight that string theory in-
cluded gravity as described by the theory of general relativity.
In the 1970s and early ’80s, string theory teetered on the
brink of oblivion. It didn’t seem to work for its original pur-
pose, which was the description of nuclear forces. While it
incorporated quantum mechanics, it seemed likely to have
a subtle inconsistency called an anomaly. An example of an
anomaly is that if there were particles similar to neutrinos, but
electrically charged, then certain types of gravitational fields
could spontaneously create electric charge. That’s bad because
quantum mechanics needs the universe to maintain a strict
balance between negative charges, like electrons, and positive
charges, like protons. So it was a big relief when, in 1984, it
was shown that string theory was free of anomalies. It was
then perceived as a viable candidate to describe the universe.
This apparently technical result started the “first super-
string revolution”: a period of frantic activity and dramatic
advances, which nevertheless fell short of its stated goal, to
produce a theory of everything. I was a kid when it got going,

3
and I lived close to the Aspen Center for Physics, a hotbed of
activity. I remember people muttering about whether super-
string theory might be tested at the Superconducting Super
Collider, and I wondered what was so super about it all. Well,
superstrings are strings with the special property of supersym-
metry. And what might supersymmetry be? I’ll try to tell you
more clearly later in this book, but for now, let’s settle for two
very partial statements. First: Supersymmetry relates particles
with different spins. The spin of a particle is like the spin of a
top, but unlike a top, a particle can never stop spinning. Sec-
ond: Supersymmetric string theories are the string theories
that we understand the best. Whereas non-supersymmetric
string theories require 26 dimensions, supersymmetric ones
only require ten. Naturally, one has to admit that even ten
dimensions is six too many, because we perceive only three
of space and one of time. Part of making string theory into a
theory of the real world is somehow getting rid of those extra
dimensions, or finding some useful role for them.
For the rest of the 1980s, string theorists raced furiously
to uncover the theory of everything. But they didn’t under-
stand enough about string theory. It turns out that strings are
not the whole story. The theory also requires the existence of
branes: objects that extend in several dimensions. The sim-
plest brane is a membrane. Like the surface of a drum, a
membrane extends in two spatial dimensions. It is a surface
that can vibrate. There are also 3-branes, which can fill the
three dimensions of space that we experience and vibrate in
the additional dimensions that string theory requires. There
can also be 4-branes, 5-branes, and so on up to 9-branes. All
of this starts to sound like a lot to swallow, but there are solid
reasons to believe that you can’t make sense of string theory
without all these branes included. Some of these reasons have

4
to do with “string dualities.” A duality is a relation between
two apparently different objects, or two apparently differ-
ent viewpoints. A simplistic example is a checkerboard. One
view is that it’s a red board with black squares. Another view
is that it’s a black board with red squares. Both viewpoints
(made suitably precise) provide an adequate description of
what a checkerboard looks like. They’re different, but related
under the interchange of red and black.
The middle 1990s saw a second superstring revolution,
based on the emerging understanding of string dualities and
the role of branes. Again, efforts were made to parlay this
new understanding into a theoretical framework that would
qualify as a theory of everything. “Everything” here means
all the aspects of fundamental physics we understand and
have tested. Gravity is part of fundamental physics. So are
electromagnetism and nuclear forces. So are the particles,
like electrons, protons, and neutrons, from which all atoms
are made. While string theory constructions are known that
reproduce the broad outlines of what we know, there are
some persistent difficulties in arriving at a fully viable theory.
At the same time, the more we learn about string theory, the
more we realize we don’t know. So it seems like a third
superstring revolution is needed. But there hasn’t been one
yet. Instead, what is happening is that string theorists are
trying to make do with their existing level of understanding
to make partial statements about what string theory might
say about experiments both current and imminent. The
most vigorous efforts along these lines aim to connect string
theory with high-energy collisions of protons or heavy ions.
The connections we hope for will probably hinge on the
ideas of super
symmetry, or extra dimensions, or black hole
horizons, or maybe all three at once.

5
Now that we’re up to the modern day, let’s detour to con-
sider the two types of collisions I just mentioned.
Proton collisions will soon be the main focus of experi-
mental high-energy physics, thanks to a big experimental fa-
cility near Geneva called the Large Hadron Collider (LHC).
The LHC will accelerate protons in counter-rotating beams
and slam them together in head-on collisions near the speed
of light. This type of collision is chaotic and uncontrolled.
What experimentalists will look for is the rare event where
a collision produces an extremely massive, unstable particle.
One such particle—still hypothetical—is called the Higgs
boson, and it is believed to be responsible for the mass of the
electron. Supersymmetry predicts many other particles, and
if they are discovered, it would be clear evidence that string
theory is on the right track. There is also a remote possi-
bility that proton-proton collisions will produce tiny black
holes whose subsequent decay could be observed.
In heavy ion collisions, a gold or lead atom is stripped of all
its electrons and whirled around the same machine that carries
out proton-proton collisions. When heavy ions collide head-
on, it is even more chaotic than a proton-proton collision. It’s
believed that protons and neutrons melt into their constituent
quarks and gluons. The quarks and gluons then form a fluid,
which expands, cools, and eventually freezes back into the
particles that are then observed by the detectors. This fluid
is called the quark-gluon plasma. The connection with string
theory hinges on comparing the quark-gluon plasma to a black
hole. Strangely, the kind of black hole that could be dual to the
quark-gluon plasma is not in the four dimensions of our every-
day experience, but in a five-dimensional curved spacetime.
It should be emphasized that string theory’s connections to
the real world are speculative. Supersymmetry might simply

6
not be there. The quark-gluon plasma produced at the LHC
may really not behave much like a five-
dimensional black
hole. What is exciting is that string theorists are placing
their bets, along with theorists of other stripes, and holding
their breaths for experimental discoveries that may vindicate
or shatter their hopes.
This book builds up to some of the core ideas of modern
string theory, including further discussion of its potential
applications to collider physics. String theory rests on two
foundations: quantum mechanics and the theory of relativ-
ity. From those foundations it reaches out in a multitude of
directions, and it’s hard to do justice to even a small fraction
of them. The topics discussed in this book represent a slice
across string theory that largely avoids its more mathemati-
cal side. The choice of topics also reflects my preferences and
prejudices, and probably even the limits of my understand-
ing of the subject.
Another choice I’ve made in writing this book is to dis-
cuss physics but not physicists. That is, I’m going to do my
best to tell you what string theory is about, but I’m not going
to tell you about the people who figured it all out (although
I will say up front that mostly it wasn’t me). To illustrate
the difficulties of doing a proper job of attributing ideas to
people, let’s start by asking who figured out relativity. It was
Albert Einstein, right? Yes—but if we just stop with that
one name, we’re missing a lot. Hendrik Lorentz and Henri
Poincaré did important work that predated Einstein; Her-
mann Minkowski introduced a crucially important math-
ematical framework; David Hilbert independently figured
out a key building block of general relativity; and there are
several more important early figures like James Clerk Max-
well, George FitzGerald, and Joseph Larmor who deserve

7
mention, as well as later pioneers like John Wheeler and
Subrahmanyan Chandrasekhar. The development of quan-
tum mechanics is considerably more intricate, as there is no
single figure like Einstein whose contributions tower above
all others. Rather, there is a fascinating and heterogeneous
group, including Max Planck, Einstein, Ernest Ruther
ford,
Niels Bohr, Louis de Broglie, Werner Heisenberg, Erwin
Schrödinger, Paul Dirac, Wolfgang Pauli, Pascual Jordan,
and John von Neumann, who contributed in essential
ways—and sometimes famously disagreed with one another.
It would be an even more ambitious project to properly as-
sign credit for the vast swath of ideas that is string theory.
My feeling is that an attempt to do so would actually de-
tract from my primary aim, which is to convey the ideas
themselves.
The aim of the first three chapters of this book is to in-
troduce ideas that are crucial to the understanding of string
theory, but that are not properly part of it. These ideas—
energy, quantum mechanics, and general relativity—are
more important (so far) than string theory itself, because we
know that they describe the real world. Chapter 4, where
I introduce string theory, is thus a step into the unknown.
While I attempt in chapters 4, 5, and 6 to make string the-
ory, D-branes, and string dualities seem as reasonable and
well motivated as I can, the fact remains that they are un-
verified as descriptions of the real world. Chapters 7 and
8 are devoted to modern attempts to relate string theory
to experiments involving high-energy particle collisions.
Supersymmetry, string dualities, and black holes in a fifth
dimension all figure in string theorists’ attempts to under-
stand what is happening, and what will happen, in particle
accelerators.

8
I N T R O D U C T I O N
In various places in this book, I quote numerical values
for physical quantities: things like the energy released in
nuclear fission or the amount of time dilation experienced
by an Olympic sprinter. Part of why I do this is that phys-
ics is a quantitative science, where the numerical sizes of
things matter. However, to a physicist, what’s usually most
interesting is the approximate size, or order of magnitude,
of a physical quantity. So, for example, I remark that the
time dilation experienced by an Olympic sprinter is about a
part in 1015 even though a more precise estimate, based on a
speed of 10 m/s, is a part in 1.8 × 1015. Readers wishing to
see more precise, explicit, and/or extended versions of the
calculations I describe in the book can visit this website:
http://press.princeton.edu/titles/9133.html.
Where is string theory going? String theory promises to
unify gravity and quantum mechanics. It promises to pro-
vide a single theory encompassing all the forces of nature. It
promises a new understanding of time, space, and additional
dimensions as yet undiscovered. It promises to relate ideas as
seemingly distant as black holes and the quark-gluon plasma.
Truly it is a “promising” theory!
How can string theorists ever deliver on the promise
of their field? The fact is, much has been delivered. String
theory does provide an elegant chain of reasoning starting
with quantum mechanics and ending with general relativ-
ity. I’ll describe the framework of this reasoning in chapter
4. String theory does provide a provisional picture of how
to describe all the forces of nature. I’ll outline this picture in
chapter 7 and tell you some of the difficulties with making it
more precise. And as I’ll explain in chapter 8, string theory
calculations are already being compared to data from heavy
ion collisions.

9
I don’t aim to settle any debates about string theory in
this book, but I’ll go so far as to say that I think a lot of the
disagreement is about points of view. When a noteworthy
result comes out of string theory, a proponent of the theory
might say, “That was fantastic! But it would be so much bet-
ter if only we could do thus-and-such.” At the same time, a
critic might say, “That was pathetic! If only they had done
thus-and-such, I might be impressed.” In the end, the pro-
ponents and the critics (at least, the more serious and in-
formed members of each camp) are not that far apart on
matters of substance. Everyone agrees that there are some
deep mysteries in fundamental physics. Nearly everyone
agrees that string theorists have mounted serious attempts to
solve them. And surely it can be agreed that much of string
theory’s promise has yet to be delivered upon.

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And this was so. Bruce was a different lad, from then on. His face
was always smiling, as it had been before his trouble.
“I never can thank you, Tom, for what you did for me,” he said.
“Only for you Skeel would have carried out his threat, and his
forgery never would have been discovered in time to prevent my
disgrace. But I’ve made a clean breast of it to dad, and though he
gave me a hard calling down, he’s forgiven me. Oh, I feel so glad!”
“And so do I,” added Tom. “We’re going to have a new Latin prof.
I understand. A jolly young fellow.”
“That’s good. Here comes Demy. I wonder what he wants?” spoke
Bruce, as the studious janitor approached, with a book as usual.
“Well, what is it?” asked the Senior.
“I fear I have made a grave mistake,” said Mr. Miller. “In
announcing the disappearance of Professor Skeel the other day I
used the Latin word vanesco. I see now that I used the wrong tense.
Will you kindly set me right.”
“Demy!” exclaimed Tom, “if you will kindly follow the example of
Professor Skeel, and vamoose, it will be all the same. We’ll give you
a Latin lesson later. And, in the meanwhile, here is a dollar to buy a
dictionary,” and Tom passed over a bill to the man who was always a
friend to the students.
As for Professor Skeel he was not heard of again for some time.
But the lads of Elmwood Hall did not care. They had Tom Fairfield,
who became more of a leader than ever after his successful strike.
As for Sam Heller, he led a miserable life as a Freshman—ignored by
nearly all.
“Come on in to town,” invited Bruce that night. “I’ll treat you
fellows to a good feed, Tom. And I’ve fixed it with Merry, so we
won’t have to hurry back.”
“Good!” exclaimed our hero, and on his way with his chums to a
good time, we will say good-bye to him for a time.

Polly says “JELL-O for me”
If cast upon a desert isle
Like Crusoe long ago,
How dull the diet soon would be
How jaded you would grow!
Your gun would get you meat enough,
Your line would catch your fish,
But what a hunger you would have
For some nice snappy dish.
Then just suppose one sunny day,
While striding on the beach,
You’d hear your jolly Polly give
A most delightful screech.
And this is what old Pol would say——
For he’s a jolly fellow——
“I don’t want crackers, no-sir-ee,
When I can feast on Jell-O.

“We’ve lots or nuts on this here isle;
Go pick ’em, Mr. Crusoe,
We’d like to eat a good dessert,
Get busy and we’ll do so.”
There are six pure fruit flavors of Jell-O:
Strawberry, Raspberry, Lemon, Orange, Cherry,
Chocolate. Every child wants the little book,
“Miss Jell-O Gives a Party,” and we will send it
free upon request, but be sure your name and
address are plainly written.
America’s most famous dessert
Jell-O
THE JELL-O COMPANY. Inc.
Le Roy, N. Y.
Bridgeburg, Ont.
Reprinted by permission of John Martin’s Book, the Child’s
Magazine
THE BOYS’ OUTING LIBRARY
12mo. Cloth. Illustrated. Jacket in full color.
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THE SADDLE BOYS SERIES
By CAPT. JAMES CARSON

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The Speedwell Boys on Motorcycles
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THE TOM FAIRFIELD SERIES
By ALLEN CHAPMAN
Tom Fairfield’s School Days
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THE FRED FENTON ATHLETIC SERIES
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CUPPLES & LEON COMPANY, Publishers New York
THE BOY RANCHERS SERIES
By WILLARD F. BAKER
12mo. Cloth. Illustrated. Jacket in full colors
Price per volume, 65 cents, postpaid
Stories of the great west, with cattle ranches
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or Solving the Mystery at Diamond X
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or The Water Fight at Diamond X

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or Diamond X and the Lost Mine
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or Diamond X and the Chinese Smugglers
The boy ranchers help capture Delton’s gang who were
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midst of a series of strange events and into the companionship
of strange persons, not the least of whom was the man with the
wooden leg. But Bob got the best of this vindictive individual,
and solved the mystery of the log cabin, showing his friends
how the secret entrance to the house was accomplished.
CUPPLES & LEON COMPANY, PUBLISHERS New York

THE COLLEGE SPORTS SERIES
By LESTER CHADWICK
12mo. Cloth. Illustrated. Jacket in Colors
Price per volume, $1.00, postpaid
Mr. Chadwick has played on the diamond and
on the gridiron himself.
1. THE RIVAL PITCHERS
A Story of College Baseball
Tom Parsons, a “hayseed,” makes good on the
scrub team of Randall College.
2. A QUARTERBACK’S PLUCK
A Story of College Football
A football story, told in Mr. Chadwick’s best style, that is
bound to grip the reader from the start.
3. BATTING TO WIN
A Story of College Baseball
Tom Parsons and his friends Phil and Sid are the leading
players on Randall College team. There is a great game.
4. THE WINNING TOUCHDOWN
A Story of College Football
After having to reorganize their team at the last moment,
Randall makes a touchdown that won a big game.
5. FOR THE HONOR OF RANDALL.
A Story of College Athletics

The winning of the hurdle race and long-distance run is
extremely exciting.
6. THE EIGHT-OARED VICTORS
A Story of College Water Sports
Tom, Phil and Sid prove as good at aquatic sports as they are
on track, gridiron and diamond.
Transcriber’s Notes:
Printer, punctuation and spelling inaccuracies were
silently corrected, except as indicated below.
Archaic and variable spelling is preserved.
Variations in hyphenation and compound words
have been preserved.
The Author’s long dash style has been retained.
Inconsistencies in formatting and punctuation of
individual advertisements have been retained.
Page numbers in the Table of Contents for
Chapters IV and V have been changed to reflect the
actual beginning page number in the text.

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