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CHAPTER 1 Introduction
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Type II-A string theory This version of string theory also includes supersymmetry, and open and closed strings. Open strings in type II-A string theory have their ends attached to higher-dimensional objects called D-Branes. Fermions in this theory are not chiral. Type II-B string theory fermions. Like type II-A string theory, but it has chiral
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Heterotic string theory Includes supersymmetry and only allows closed strings. Has a gauge group called E8 E8. The left- and rightmoving modes on the string actually require different numbers of spacetime dimensions (10 and 26). We will see later that there are actually two heterotic string theories.
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M-THEORY
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All these string theories might seem confusing, and make the whole enterprise seem like a stab in the dark. However, as we go through the book we will learn about the different dualities that connect the different types of string theories. These go by the names of S duality and T duality. Since these dualities exist, there has been speculation that there is an underlying, more fundamental theory. It does by the odd name of M-theory but M does not really have any agreed upon or speci c meaning (perhaps mother of all theories). One concept in M-theory is that the space-time manifold (i.e., its structure) is not assumed a priori but rather emerges from the vacuum. One concrete manifestation of M-theory is based on matrix mechanics, the kind you are used to from ordinary quantum mechanics. In this context M really means something, and we call it matrix theory. In this theory, if we compactify (i.e., make really tiny) n spatial dimensions on a torus, we get out a dual matrix theory that is just an ordinary quantum eld theory in n + 1 space-time dimensions.
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D-BRANES
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A D-brane, mentioned in our discussion of string theory types, is an extension of the common sense notion of a membrane, which is a two-dimensional brane or 2-brane. A string can be though of as a one-dimensional brane or 1-brane. So a p-brane is an object with p spatial dimensions. D-branes are important in string theory because the ends of fundamental strings can attach to them. It is believed that quantum elds described by Yang-Mills type theories (such as electromagnetism) involve strings that are attached by D-branes. This idea has great explanatory power, because gravitons, the quantum
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of gravity, are not attached to D-branes. They can travel or leak off a D-brane, so we don t see as many of them. This explains what until now has been a great mystery, why electromagnetism (and the other known forces) is so much stronger than gravity. So this picture of the universe has a three-dimensional brane (or 3D-brane) embedded in a higher-dimensional space-time called the bulk. Since we interact with the physical world primarily through electromagnetic forces (light, chemical reactions, etc.), which are mediated by particles that are really strings stuck to the brane, we experience the world as having three spatial dimensions. Gravity is mediated by strings that can leave the brane and travel off into the bulk, so we see it as a much weaker force. If we could probe the bulk somehow, we would see that gravity is actually comparable in strength.
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HIGHER DIMENSIONS
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We live in a world with three spatial dimensions. In a nutshell this means that there are three distinct directions through which movement is possible: up-down, leftright, and forward-backward. In addition, we have the ow of time (forward only as far as we know). Mathematically, this gives us the relativistic description of coordinates ( x, y, z, t ). It is possible to imagine a world where one of the spatial directions or dimensions have been removed (say up-down). Such a two-dimensional world was described by Edward Abbott in his classic Flatland. What if instead, we added dimensions This idea is actually pretty useful in physics, because it provides a pathway toward unifying different physical theories. This kind of thinking was originally put forward by two physicists named Kaluza and Klein in the 1920s. Their idea was to bring gravity and electromagnetism into a single theoretical framework by imagining that these two theories were four-dimensional limits of a ve-dimensional supertheory. This idea did not work out, because back then people did not know about quantum eld theory and so did not have a complete picture of particle interactions, and did not know that the fully correct description of electromagnetic interactions is provided by quantum electrodynamics. But this idea has a lot of appeal and reemerged in string theory. Kaluza and Klein had to explain why we don t see the higher dimension, and hit upon the idea of compacti cation a procedure where we make the higher dimensions so small they are not detectable at lower energy (i.e., on the kind of energy scales that we live in). If they are small enough, the extra dimensions can t be noticed or detected scienti cally without the existence of the appropriate technology. If they are so small that they are on the Planck scale, we might not be able to see them at all. This concept is illustrated in Fig. 1.8.
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