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# String Theory Demystified

**by**McMahon, David

1st

### 9780071498708

0071498702

Paperback

8/21/2008

McGraw-Hill Professional

## Questions About This Book?

What version or edition is this?

This is the 1st edition with a publication date of 8/21/2008.

What is included with this book?

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## Summary

UNRAVEL the mystery of STRING THEORY Trying to understand string theory but ending up with your brain in knots? Here's your lifeline! This straightforward guide explains the fundamental principles behind this cutting-edge concept. String Theory Demystified elucidates the goal of the theory--to combine general relativity and quantum theory into a single, unified framework. You'll learn about classical strings, conformal field theory, quantization, compactification, and T duality. The book covers supersymmetry and superstrings, D-branes, the holographic principle, and cosmology. Hundreds of examples and illustrations make it easy to understand the material, and end-of-chapter quizzes and a final exam help reinforce learning. This fast and easy guide offers: Numerous figures to illustrate key concepts Sample problems with worked solutions Coverage of equations of motion, the energy-momentum tensor, and conserved currents A discussion of the Randall-Sundrum model A time-saving approach to performing better on an exam or at workSimple enough for a beginner, but challenging enough for an advanced student, String Theory Demystified is your key to comprehending this theory of everything.

## Author Biography

David McMahon (Albuquerque, NM) works as a researcher in the National Laboratories on nuclear energy. He has advanced degrees in physics and applied mathematics, and has authored several titles for McGraw-Hill, most recently: Quantum Mechanics Demystified, Relativity Demystified, Linear Algebra Demystified, Signals and Systems Demystified, and Statics and Dynamics Demystified.

## Table of Contents

Preface | p. xi |

Introduction | p. 1 |

A Quick Overview of General Relativity | p. 2 |

A Quick Primer on Quantum Theory | p. 3 |

The Standard Model | p. 8 |

Quantizing the Gravitational Field | p. 8 |

Some Basic Analysis in String Theory | p. 10 |

Unification and Fundamental Constants | p. 11 |

String Theory Overview | p. 12 |

Summary | p. 18 |

Quiz | p. 18 |

The Classical String I: Equations of Motion | p. 21 |

The Relativistic Point Particle | p. 22 |

Strings in Space-Time | p. 28 |

Equations of Motion for the String | p. 32 |

The Polyakov Action | p. 36 |

Mathematical Aside: The Euler Characteristic | p. 36 |

Light-Cone Coordinates | p. 39 |

Solutions of the Wave Equation | p. 43 |

Open Strings with Free Endpoints | p. 44 |

Closed Strings | p. 46 |

Open Strings with Fixed Endpoints | p. 47 |

Poisson Brackets | p. 49 |

Quiz | p. 49 |

The Classical String II: Symmetries and Worldsheet Currents | p. 51 |

The Energy-Momentum Tensor | p. 52 |

Symmetries of the Polyakov Action | p. 53 |

Transforming to a Flat Worldsheet Metric | p. 59 |

Conserved Currents from Poincare Invariance | p. 63 |

The Hamiltonian | p. 67 |

Summary | p. 67 |

Quiz | p. 67 |

String Quantization | p. 69 |

Covariant Quantization | p. 70 |

Light-Cone Quantization | p. 85 |

Summary | p. 87 |

Quiz | p. 87 |

Conformal Field Theory Part I | p. 89 |

The Role of Conformal Field Theory in String Theory | p. 92 |

Wick Rotations | p. 93 |

Complex Coordinates | p. 94 |

Generators of Conformal Transformations | p. 98 |

The Two-Dimensional Conformal Group | p. 100 |

Central Extension | p. 104 |

Closed String Conformal Field Theory | p. 105 |

Wick Expansion | p. 107 |

Operator Product Expansion | p. 110 |

Summary | p. 114 |

Quiz | p. 114 |

BRST Quantization | p. 115 |

BRST Operators and Introductory Remarks | p. 116 |

BRST-Invariant States | p. 118 |

BRST in String Theory-CFT | p. 120 |

BRST Transformations | p. 121 |

No-Ghost Theorem | p. 125 |

Summary | p. 125 |

Quiz | p. 126 |

RNS Superstrings | p. 127 |

The Superstring Action | p. 128 |

Conserved Currents | p. 133 |

The Energy-Momentum Tensor | p. 136 |

Mode Expansions and Boundary Conditions | p. 140 |

Super-Virasoro Generators | p. 143 |

Canonical Quantization | p. 144 |

The Super-Virasoro Algebra | p. 145 |

The Open String Spectrum | p. 147 |

GSO Projection | p. 148 |

Critical Dimension | p. 149 |

Summary | p. 150 |

Quiz | p. 150 |

Compactification and T-Duality | p. 153 |

Compactification of the 25th Dimension | p. 153 |

Modified Mass Spectrum | p. 155 |

T-Duality for Closed Strings | p. 159 |

Open Strings and T-Duality | p. 162 |

D-Branes | p. 164 |

Summary | p. 165 |

Quiz | p. 165 |

Superstring Theory Continued | p. 167 |

Superspace and Superfields | p. 168 |

Superfield for Worldsheet Supersymmetry | p. 171 |

Grassman Integration | p. 173 |

A Manifestly Supersymmetric Action | p. 174 |

The Green-Schwarz Action | p. 175 |

Space-Time Supersymmetry and Strings | p. 180 |

Light-Cone Gauge | p. 181 |

Canonical Quantization | p. 184 |

Summary | p. 185 |

Quiz | p. 186 |

A Summary of Superstring Theory | p. 187 |

A Summary of Superstring Theory | p. 187 |

Superstring Theory | p. 190 |

Dualities | p. 192 |

Quiz | p. 193 |

Type II String Theories | p. 195 |

The R and NS Sectors | p. 195 |

The Spin Field | p. 200 |

Type II A String Theory | p. 201 |

Type II B Theory | p. 203 |

The Massless Spectrum of Different Sectors | p. 203 |

Summary | p. 204 |

Quiz | p. 205 |

Heterotic String Theory | p. 207 |

The Action for SO(32) Theory | p. 208 |

Quantization of SO(32) Theory | p. 209 |

The Spectrum | p. 214 |

Compactification and Quantized Momentum | p. 216 |

Summary | p. 219 |

Quiz | p. 219 |

D-Branes | p. 221 |

The Space-Time Arena | p. 223 |

Quantization | p. 225 |

D-Branes in Superstring Theory | p. 230 |

Multiple D-Branes | p. 230 |

Tachyons and D-Brane Decay | p. 235 |

Summary | p. 237 |

Quiz | p. 237 |

Black Holes | p. 239 |

Black Holes in General Relativity | p. 240 |

Charged Black Holes | p. 243 |

The Laws of Black Hole Mechanics | p. 246 |

Computing the Temperature of a Black Hole | p. 247 |

Entropy Calculations for Black Holes with String Theory | p. 249 |

Summary | p. 253 |

Quiz | p. 253 |

The Holographic Principle and AdS/CFT Correspondence | p. 255 |

A Statement of the Holographic Principle | p. 256 |

A Qualitative Description of AdS/CFT Correspondence | p. 257 |

The Holographic Principle and M-Theory | p. 258 |

More Correspondence | p. 260 |

Summary | p. 262 |

Quiz | p. 262 |

String Theory and Cosmology | p. 265 |

Einstein's Equations | p. 266 |

Inflation | p. 266 |

The Kasner Metric | p. 268 |

The Randall-Sundrum Model | p. 273 |

Brane Worlds and the Ekpyrotic Universe | p. 275 |

Summary | p. 277 |

Quiz | p. 278 |

Final Exam | p. 279 |

Quiz Solutions | p. 285 |

Final Exam Solutions | p. 291 |

References | p. 297 |

Index | p. 299 |

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