Introduction to Superstrings and M-Theory. Author: Michio Kaku including: string field theory, multi loops, Teichmueller spaces, conformal field theory, and. Michio Kaku. Introduction to. Superstrings and. M-Theory. Second Edition. With 45 Illustrations 4 Conformal Field Theory and Kac-Moody Algebras. Introduction to Superstrings and M-Theory has ratings and 3 reviews. Robert said: Since Carl Sagan died, there is nobody out there comparable in my m.

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Every decade or so, a stunning breakthrough in string theory sends shock waves racing through the theoretical physics community, generating a feverish outpouring of papers and activity. The after- shocks of the breakthrough are even shaking other disciplines, like mathematics. Intriduction one dazzling stroke, this new M-theory has solved a series of long-standing puzzling mysteries about string theory which have dogged it from the beginning, leaving many theoretical physicists myself included!

M-theory, moreover, may even force string theory to change its name. Although many features of M-theory are still unknown, it does not seem to be a theory purely of strings. Not by any means. That may make years or decades more.

But it marks a most significant breakthrough that is already reshaping the entire field. But I do not doubt that the lion belongs to it even though he cannot at once reveal himself because of his enormous size.

The four forces gravity, electromagnetism, and the strong and weak nuclear forces would be unified by an equation perhaps one inch long. But although Einstein was the first one to set off on this noble hunt and track the footprints introductiom by the lion, he ultimately lost the trail and wandered off into the wilderness. Other giants superstrijgs 20th century physics, like Werner Heisenberg and Wolfgang Pauli, theogy joined in the hunt.

But all the easy ideas were tried and shown to be wrong. But what divides us is whether your theory is crazy enough! The trail leading to the unified field theory, in fact, is littered with the wreckage of failed expeditions and dreams.

## Introduction to Superstrings and M-Theory

This new trail leads to superstring theory, which is the best and in fact only candidate for a theory of everything. Unlike its rivals, it has survived every blistering mathematical challenge ever hurled at it. I regard this fact as one of the greatest in- sights in science ever made.

Ultimately, it may solve the nagging question of where strings come from. Einstein once asked himself if God had any choice in making the universe.

Perhaps not, so it was embarrassing for string theorists to have five different self-consistent strings, all of which can unite the two fundamental theories in physics, the theory of gravity and the quantum theory. Each of these string theories looks completely different from the others.

They are based on different symmetries, with exotic names like E 8 xE 8 and O Not only this, but superstrings are in some sense not unique: Changing light into electrons and then into gravity is one of the rather astonishing tricks performed by supersymmetry, which is the symmetry which can exchange particles with half-integral spin, like electrons and quarks, with particles of integral spin, like photons, gravitons, and W-particles.

In 11 dimensions, in fact, there are alternate super theories based on membranes as well as point particles called super- gravity.

In lower dimensions, there is moreover a whole zoo of super theories based on membranes in different dimensions. For example, point particles are 0-branes, strings are 1-branes, membranes are 2-branes, and so on. But because p-branes are horribly difficult to work with, they were long considered just a historical curiosity, a trail that led to a dead-end.

Michael Duff, in fact, has collected a whole list of unflattering comments made by referees to his National Science Foundation grant concerning his work on p- branes. One of the more charitable comments from a referee was: Why should supersymmetry allow for 5 superstrings and this peculiar, motley collection of p-branes? Now we realize that strings, supergravity, and p-branes are just different aspects of the same theory.

To see how this all fits together, let us update the famous parable of the blind wise men and the elephant. Think of the blind men on the trail of the lion. Hearing it race by, they chase after it and desperately grab onto its tail a one-brane. But then one blind man goes beyond the tail and grabs onto the ear of the lion. Just as the tail, ear, and leg tgeory different parts of supersrtings same lion, the string and various p- branes appear to be different limits of the same theory: Schwarz puts a slightly different spin on this.

The point is that they are the only ones on which we can base a perturbation theory. The simplest example introdution duality is reversing the role supersyrings electricity and magnetism in the equations discovered by James Clerk Maxwell of Cambridge University years ago.

These are the equations which govern light, TV, X-rays, superstrimgs, dynamos, motors, transformers, even the Internet and computers. This has important implications. Often, superstrinys a theory cannot be solved exactly, we use an approximation scheme.

Notice that each contribution is getting smaller and smaller, so we can in principle add them all up. For example, in archery, perturbation theory is how we aim our arrows. So at first it appears hopeless that we could ever penetrate into the non-perturbative region. For example, if every motion of our arms got bigger theoey bigger, we would never be able to zero in and hit the target with the kalu.

But notice that because of duality, a theory of small e which is easily solved is identical to a theory of large g which is difficult to solve. But since they are the same theory, we can use duality to solve for the non-perturbative region.

The first inkling that duality might apply in string theory was discovered by K. Yamasaki of Osaka Univ. This is now called T- duality: Unfortunately, T duality was still a perturbative duality. The next breakthrough came when it was shown that there was a second class of dualities, called S duality, which provided a duality between the perturbative and non-perturbative regions of string theory.

Another duality, called U duality, was even more powerful. Then Nathan Seiberg and Witten brilliantly showed how another form of duality could solve for the non-perturbative region in four dimensional supersymmetric theories. However, what finally convinced many physicists of the power of this technique was the work of Paul Townsend and Edward Wit- ten. They caught everyone by surprise by showing that there was a duality between 10 dimensional Type IIa strings and 11 dimension- al supergravity!

The non-perturbative region of Type IIa strings, which was previously a forbidden region, was revealed to be governed by 11 dimensional supergravity theory, with one dimension curled up. At this point, I remember that many physicists myself included were rubbing our eyes, not believing what we were seeing. This revived tremendous interest in 11 dimensional theories and p- branes.

### Introduction to Superstrings and M-Theory by Michio Kaku

Lurking suprestrings the 11th dimension was an entirely new theory which could reduce down to 11 dimensional supergravity as well as 10 dimensional string theory and p-brane theory.

Since string theory is really a theory of Creation, when all its beautiful symmetries were in their full glory, the only way to test it, the critics wail, is to re-create the Big Bang itself, which is impossible. Nobel Laureate Sheldon Glashow likes to ridicule superstring theory by comparing it with former Pres.

Actually, most string theorists think these criticisms are silly. They believe that the critics have missed the point.

The key point is this: If we could completely solve the theory, we should be able to extract its low energy spectrum, which should match the familiar particles we see today in the Standard Model. Thus, the problem is not building atom smashers l, light years in diameter; the real problem is raw brain power: So what would it take to actually solve the theory once and for all and end all the speculation and back-biting?

There are several approaches. The first is the most direct: I must admit that although the Standard Model is the most successful physical theory ever proposed, it is also one of the ugliest. This might be done by curling up 6 of the 10 dimensions, leaving us with a 4 dimensional theory that might resemble the Standard Model a bit.

Then try to use duality and M- theory to probe its non-perturbative region, seeing if the symmetries break in the correct fashion, giving us the correct masses of the quarks and other particles in the Standard Model. He feels that the key to solving string theory is to understand the under- lying principle behind the theory. Although physicists since Galileo knew this, Einstein was able to extract from this the Equivalence Principle. This deceptively simple statement that the laws of physics are indistinguishable locally in an accelerating or a gravitating frame led Einstein to introduce a new symmetry to physics, general co-ordinate transformations.

This in turn gave birth to the action principle behind general relativity, the most beautiful and compelling theory of gravity. Only now are we trying to quantize the theory to make it compatible with the other forces. So the evolution of this theory can be summarized as: Unfortunately, this 12 dimensional theory is rather strange: Imagine trying to live in a world with two times!

It would put an episode of Twilight Zone to shame. So is the final theory 10, 11, or 12 dimensional? Schwarz, for one, feels that the final version of M-theory may not even have any fixed dimension. He feels that the true theory may be independent of any dimensionality of space-time, and that 11 dimensions only emerges once one tries to solve it. I asked some of the leaders in this field to respond to this question. Although they are all enthusiastic supporters of this revolution, they are still cautious about predicting the future.

Townsend believes that we are in a stage similar to the old quantum era of the Bohr atom, just before the full elucidation of quantum mechanics. I am personally agnostic on this point.

In any case, finding it would be a landmark in human intellectual history. For the first time, we can see the outline of the lion, and it is magnificent. One day, we will hear it roar. For the complete library of books by Dr. Michio Kaku, click here. The Mother of all SuperStrings An introduction to M-Theory Every decade or so, a stunning breakthrough in string theory sends shock waves racing through the theoretical physics community, generating a feverish outpouring of papers and activity.

Evolving Backwards So what would it take to actually solve the theory once and for all and end all the speculation and back-biting?