| Preface | p. ix |
| An elementary introduction to branes in string theory | p. 1 |
| Introduction | p. 3 |
| Branes in string theory | p. 6 |
| The superstring effective actions of type II | p. 6 |
| Type IIA | p. 6 |
| Type IIB | p. 8 |
| General construction | p. 11 |
| Explicit solutions | p. 13 |
| Fundamental string | p. 13 |
| NS 5-brane | p. 14 |
| D p-branes | p. 16 |
| The geometry of the D3-brane of type IIB | p. 18 |
| The boundary state description of D-branes | p. 21 |
| The boundary state with an external field | p. 21 |
| The effective action of D-branes | p. 25 |
| Classical D-branes from the boundary state | p. 30 |
| References | p. 35 |
| Physical aspects | p. 37 |
| Two-dimensional conformal field theory on open and unoriented surfaces | p. 39 |
| Introduction | p. 39 |
| General properties of two-dimensional CFT | p. 40 |
| The stress-energy tensor in two dimensions | p. 40 |
| Rational conformal field theories | p. 44 |
| Non-Abelian conformal current algebras | p. 46 |
| Partition function, modular invariance | p. 48 |
| Correlation functions in current algebra models | p. 51 |
| Properties of the chiral conformal blocks | p. 51 |
| Regular basis of 4-point functions in the SU (2) model | p. 53 |
| Matrix representation of the exchange algebra | p. 55 |
| Two-dimensional braid invariant Green functions | p. 57 |
| CFT on surfaces with holes and crosscaps | p. 60 |
| Open sector, sewing constraints | p. 61 |
| Closed unoriented sector, crosscap constraint | p. 69 |
| Partition functions | p. 73 |
| Klein bottle projection | p. 73 |
| Annulus partition function | p. 75 |
| Mobius strip projection | p. 77 |
| Solutions for the partition functions | p. 79 |
| Acknowledgments | p. 82 |
| References | p. 83 |
| Topics in string tachyon dynamics | p. 86 |
| Introduction | p. 86 |
| Why tachyons? | p. 88 |
| Tachyons in AdS: The c = 1 barrier | p. 89 |
| Tachyon [sigma]-model beta-functions | p. 91 |
| Open strings and cosmological constant: the Fischler-Susskind mechanism | p. 92 |
| Fischler-Susskind mechanism: closed-string case | p. 92 |
| Open-string contribution to the cosmological constant: the filling brane | p. 95 |
| The effective action | p. 97 |
| A warming-up exercise | p. 97 |
| The effective action | p. 99 |
| Non-critical dimension and tachyon condensation | p. 103 |
| D-branes, tachyon condensation and K-theory | p. 105 |
| Extended objects and topological stability | p. 105 |
| A gauge theory analogue for D-branes in type II strings | p. 105 |
| K-theory version of Sen's conjecture | p. 107 |
| Type IIA strings | p. 109 |
| Some final comments on gauge theories | p. 114 |
| Acknowledgments | p. 114 |
| References | p. 115 |
| Mathematical developments | p. 119 |
| Deformation theory, homological algebra and mirror symmetry | p. 121 |
| Introduction | p. 121 |
| Classical deformation theory | p. 125 |
| Holomorphic structure on vector bundles | p. 125 |
| Families of holomorphic structures on vector bundles | p. 128 |
| Cohomology and deformations | p. 130 |
| Bundle valued harmonic forms | p. 134 |
| Construction of a versal family and Feynman diagrams | p. 136 |
| The Kuranishi family | p. 140 |
| Formal deformations | p. 146 |
| Homological algebra and deformation theory | p. 152 |
| Homotopy theory of A[subscript infinity] and L[subscript infinity] algebras | p. 152 |
| Maurer-Cartan equation and moduli functors | p. 159 |
| Canonical model, Kuranishi map and moduli space | p. 163 |
| Superspace and odd vector fields--an alternative formulation of L[subscript infinity] algebras | p. 172 |
| Application to mirror symmetry | p. 173 |
| Novikov rings and filtered A[subscript infinity], L[subscript infinity] algebras | p. 173 |
| Review of a part of global symplectic geometry | p. 176 |
| From Lagrangian submanifold to A[subscript infinity] algebra | p. 183 |
| Maurer-Cartan equation for filtered A[subscript infinity] algebras | p. 190 |
| Homological mirror symmetry | p. 198 |
| References | p. 205 |
| Large N dualities and transitions in geometry | p. 210 |
| Geometry and topology of transitions | p. 212 |
| The local topology of a conifold transition | p. 214 |
| Transitions of Calabi-Yau threefolds | p. 221 |
| Transitions and mirror symmetry | p. 222 |
| Transitions, black holes etc | p. 223 |
| Chern-Simons theory | p. 224 |
| Chern-Simons' form and action | p. 226 |
| The Hamiltonian formulation of the Chern-Simons QFT (following Witten's canonical quantization) | p. 229 |
| Computability and link invariants | p. 234 |
| The Gopakumar-Vafa conjecture | p. 242 |
| Matching the free energies | p. 243 |
| The matching of expectation values | p. 248 |
| Lifting to M-theory | p. 253 |
| Riemannian Holonomy, G[subscript 2] manifolds and Calabi-Yau, revisited | p. 254 |
| The geometry | p. 256 |
| Branes and M-theory lifts | p. 258 |
| M-theory lift and M-theory flop | p. 259 |
| Appendix: Some notation on singularities and their resolutions | p. 261 |
| Appendix: More on the Greene-Plesser construction | p. 263 |
| Appendix: More on transitions in superstring theory | p. 264 |
| Appendix: Principal bundles, connections etc | p. 265 |
| Appendix: More on Witten's open-string theory interpretation of QFT | p. 271 |
| References | p. 274 |
| Index | p. 279 |
| Table of Contents provided by Syndetics. All Rights Reserved. |
