9780750308632

Geometry and Physics of Branes

by ;
  • ISBN13:

    9780750308632

  • ISBN10:

    075030863X

  • Edition: 1st
  • Format: Hardcover
  • Copyright: 2002-11-05
  • Publisher: CRC Press

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Summary

This book provides a review of several aspects of branes. It includes five contributions by leading scientists in the field: a general introduction to branes in string theory and four more specialized topics, ranging from the mathematical aspects related to homological mirror symmetry to more physical issues on string tachyon dynamics, two dimensional conformal field theory and large N dualities.

Table of Contents

Preface ix
PART 1 An elementary introduction to branes in string theory 1(36)
Alberto Lerda
Introduction
3(3)
Branes in string theory
6(15)
The superstring effective actions of type II
6(5)
Type IIA
6(2)
Type IIB
8(3)
General construction
11(2)
Explicit solutions
13(8)
Fundamental string
13(1)
NS 5-brane
14(2)
Dp-branes
16(2)
The geometry of the D3-brane of type IIB
18(3)
The boundary state description of D-branes
21(4)
The boundary state with an external field
21(4)
The effective action of D-branes
25(5)
Classical D-branes from the boundary state
30(7)
References
35(2)
PART 2 Physical aspects 37(82)
Yassen Stanev
Cesar Gomez
Pedro Resco
Two-dimensional conformal field theory on open and unoriented surfaces
39(47)
Introduction
39(1)
General properties of two-dimensional CFT
40(11)
The stress-energy tensor in two dimensions
40(4)
Rational conformal field theories
44(2)
Non-Abelian conformal current algebras
46(2)
Partition function, modular invariance
48(3)
Correlation functions in current algebra models
51(9)
Properties of the chiral conformal blocks
51(2)
Regular basis of 4-point functions in the SU (2) model
53(2)
Matrix representation of the exchange algebra
55(2)
Two-dimensional braid invariant Green functions
57(3)
CFT on surfaces with holes and crosscaps
60(13)
Open sector, sewing constraints
61(8)
Closed unoriented sector, crosscap constraint
69(4)
Partition functions
73(13)
Klein bottle projection
73(2)
Annulus partition function
75(2)
Mobius strip projection
77(2)
Solutions for the partition functions
79(3)
Acknowledgments
82(1)
References
83(3)
Topics in string tachyon dynamics
86(33)
Introduction
86(2)
Why tachyons?
88(1)
Tachyons in AdS: The c = 1 barrier
89(2)
Tachyon σ-model beta-functions
91(1)
Open strings and cosmological constant: the Fischler-Susskind mechanism
92(5)
Fischler-Susskind mechanism: closed-string case
92(3)
Open-string contribution to the cosmological constant: the filling brane
95(2)
The effective action
97(8)
A warming-up exercise
97(2)
The effective action
99(4)
Non-critical dimension and tachyon condensation
103(2)
D-branes, tachyon condensation and K-theory
105(9)
Extended objects and topological stability
105(1)
A gauge theory analogue for D-branes in type II strings
105(2)
K-theory version of Sen's conjecture
107(2)
Type IIA strings
109(5)
Some final comments on gauge theories
114(5)
Acknowledgments
114(1)
References
115(4)
PART 3 Mathematical developments 119(160)
Kenji Fukaya
Antonella Grassi
Michele Rossi
Deformation theory, homological algebra and mirror symmetry
121(89)
Introduction
121(4)
Classical deformation theory
125(27)
Holomorphic structure on vector bundles
125(3)
Families of holomorphic structures on vector bundles
128(2)
Cohomology and deformations
130(4)
Bundle valued harmonic forms
134(2)
Construction of a versal family and Feynman diagrams
136(4)
The Kuranishi family
140(6)
Formal deformations
146(6)
Homological algebra and deformation theory
152(21)
Homotopy theory of A∞ and L∞ algebras
152(7)
Maurer-Cartan equation and moduli functors
159(4)
Canonical model, Kuranishi map and moduli space
163(9)
Superspace and odd vector fields---an alternative formulation of L∞ algebras
172(1)
Application to mirror symmetry
173(37)
Novikov rings and filtered A∞, L∞ algebras
173(3)
Review of a part of global symplectic geometry
176(7)
From Lagrangian submanifold to A∞ algebra
183(7)
Maurer-Cartan equation for filtered A∞ algebras
190(8)
Homological mirror symmetry
198(7)
References
205(5)
Large N dualities and transitions in geometry
210(69)
Geometry and topology of transitions
212(12)
The local topology of a confifold transition
214(7)
Transitions of Calabi-Yau threefolds
221(1)
Transitions and mirror symmetry
222(1)
Transitions, black holes etc
223(1)
Chern-Simons theory
224(18)
Chern-Simons' form and action
226(3)
The Hamiltonian formulation of the Chern-Simons QFT (following Witten's canonical quantization)
229(5)
Computability and link invariants
234(8)
The Gopakumar-Vafa conjecture
242(11)
Matching the free energies
243(5)
The matching of expectation values
248(5)
Lifting to M-theory
253(8)
Riemannian Holonomy, G2 manifolds and Calabi-Yau, revisited
254(2)
The geometry
256(2)
Branes and M-theory lifts
258(1)
M-theory lift and M-theory flop
259(2)
Appendix: Some notation on singularities and their resolutions
261(2)
Appendix: More on the Greene-Plesser construction
263(1)
Appendix: More on transitions in superstring theory
264(1)
Appendix: Principal bundles, connections etc
265(6)
Appendix: More on Witten's open-string theory interpretation of QFT
271(8)
References
274(5)
Index 279

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