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CHAPTER 1 Introduction
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Close up, we see the full dimension of a cylinder
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If the radius of the cylinder is very small, from far away the cylinder appears onedimensional, as a line
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Figure 1.8 Compacti cation explains why we may not be aware of extra spatial dimensions even if they exist. If the radius of a cylinder is very small, from far away it looks like a line.
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String theory requires the existence of extra spatial dimensions for technical reasons that we will discuss in later chapters. An interesting side effect of these extra dimensions is that another mystery of particle physics is done away with. Experimentalists have worked out that there are three families of particles. For example, when considering leptons, there is the electron and its corresponding neutrino. But there are also the heavy electrons known as the muon and the tau, together with their corresponding neutrinos, that are really just duplicates of the electron. The same situation exists for the quarks. Why are there three particle families And why are there the types of particle interactions that we see It turns out that higher spatial dimensions together with string theory may provide an answer. The way that you compactify the extra dimensions (the topology) determines the numbers and types of particles seen in the universe. In string theory this results from the way that the strings can wrap around the compacti ed dimensions, determining what vibrational modes are possible in the string and hence what types of particles are possible. One important compacti ed manifold that we will see is called the Calabi-Yau manifold. A Calabi-Yau manifold that compacti es six spatial dimensions and leaves three spatial dimensions macroscopic plus time gives a ten-dimensional universe as required by most of the string theories. A key aspect of Calabi-Yau manifolds is that they break symmetries. Thus another mystery of particle physics is explained, so-called spontaneous symmetry breaking (see Quantum Field Theory Demysti ed for a description of symmetry breaking).
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String Theory Demysti ed
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Summary
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Quantum mechanics and general relativity were the major developments in theoretical physics in the twentieth century. Unifying them into a single theoretical framework has proven extremely challenging, if not impossible. This is because the resulting quantum theories are plagued by in nities that result from the fact that interactions take place at a single mathematical point (zero distance scale). By spreading out the interactions, string theory offers the hope of developing not only a uni ed theory of particle physics, but a nite theory of quantum gravity.
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Quiz
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1. If = 4 J + D 8 > 0 and p (a) the loop integral is convergent. (b) the loop integral diverges. (c) the loop integral can be calculated, but the results are meaningless. 2. The scale of the Planck length and Planck mass tell us that quantum gravity (a) operates on small-distance and high-energy scales. (b) is nonsensical. (c) operates on small-distance and small-energy scales. (d) operates on large-distance and small-energy scales. 3. Perturbation theory is possible in quantum electrodynamics because (a) EM > 1 (b) EM = 1 (c) EM < 1 (d) Perturbation theory is not possible in quantum electrodynamics 4. The quantum uncertainty relations are modi ed in string theory as (a) x (b) x (c) x (d) x p p p + p p p then
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CHAPTER 1 Introduction
5. The minimum distance scale in string theory is about 1 (a) xmin 2 (b) xmin 2 TS (c) xmin 0 (d) xmin = 2 TS
6. The topology of compacti ed dimensions (a) determines the types of particles seen in the universe. (b) has no impact on particle interactions. (c) restores symmetries in quantum eld theories. 7. Heterotic string theory has the gauge group (a) E6 E6 (b) SU( 32 ) (c) E8 E8 (d) SO(16 ) 8. String theory explains the difference between electromagnetism and gravity as (a) String theory provides the uni cation energy of gravity and electromagnetism. (b) Gravitons are not connected to the brane, so can leak off into the bulk making gravity appear much weaker than electromagnetism. (c) Photons leak off into the bulk, making electromagnetic phenomena more prominent. 9. Bosonic string theory is not realisitic because (a) it includes 26 space-time dimensions. (b) it does not allow Calabi-Yau compacti cation. (c) it does not include fermions, so cannot describe matter. (d) it lacks a E8 E8 symmetry group. 10. In string theory particle decay is explained by (a) a string splitting apart into multiple daughter strings. (b) it remains poorly understood. (c) quantum tunneling through the string potential. (d) strong vibrational modes that decouple the string.
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