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E-raamat: D-Branes

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D-branes represent a key theoretical tool in the understanding of strongly coupled superstring theory and M-theory. They have led to many striking discoveries, including the precise microphysics underlying the thermodynamic behaviour of certain black holes, and remarkable holographic dualities between large-N gauge theories and gravity. This book provides a self-contained introduction to the technology of D-branes, presenting the recent developments and ideas in a pedagogical manner. It is suitable for use as a textbook in graduate courses on modern string theory and theoretical particle physics, and will also be an indispensable reference for seasoned practitioners. The introductory material is developed by first starting with the main features of string theory needed to get rapidly to grips with D-branes, uncovering further aspects while actually working with D-branes. Many advanced applications are covered, with discussions of open problems which could form the basis for other avenues of research.

Arvustused

"...the most up-to-date string text available. It is an excellent resource..." Donald Marolf, University of California Santa Barbara, American Journal of Physics "D-Branes is an excellent complement to other existing texts on string theory..." Physics Today

Muu info

Self-contained and pedagogical introduction to key string theory ideas and techniques needed to understand D-branes.
List of inserts
xviii
Preface xx
Overview and overture
1(23)
The classical dynamics of geometry
1(6)
Gravitons and photons
7(4)
Beyond classical gravity: perturbative strings
11(4)
Beyond perturbative strings: branes
15(4)
The quantum dynamics of geometry
19(1)
Things to do in the meantime
20(2)
On with the show
22(2)
Relativistic strings
24(46)
Motion of classical point particles
24(3)
Two actions
24(2)
Symmetries
26(1)
Classical bosonic strings
27(13)
Two actions
27(2)
Symmetries
29(1)
String equations of motion
30(1)
Further aspects of the two dimensional perspective
31(4)
The stress tensor
35(1)
Gauge fixing
35(2)
The mode decomposition
37(1)
Conformal invariance as a residual symmetry
37(1)
Some Hamiltonian dynamics
38(2)
Quantised bosonic strings
40(7)
The constraints and physical states
41(1)
The intercept and critical dimensions
42(3)
A glance at more sophisticated techniques
45(2)
The sphere, the plane and the vertex operator
47(4)
States and operators
48(3)
Chan--Paton factors
51(1)
Unoriented strings
52(4)
Unoriented open strings
52(2)
Unoriented closed strings
54(1)
World-sheet diagrams
55(1)
Strings in curved backgrounds
56(5)
A quick look at geometry
61(9)
Working with the local tangent frames
61(2)
Differential forms
63(2)
Coordinate vs. orthonormal bases
65(2)
The Lorentz group as a gauge group
67(1)
Fermions in curved spacetime
68(1)
Comparison to differential geometry
68(2)
A closer look at the world-sheet
70(24)
Conformal invariance
70(10)
Diverse dimensions
70(3)
The special case of two dimensions
73(1)
States and operators
74(1)
The operator product expansion
75(1)
The stress tensor and the Virasoro algebra
76(4)
Revisiting the relativistic string
80(5)
Fixing the conformal gauge
85(2)
Conformal ghosts
85(1)
The critical dimension
86(1)
The closed string partition function
87(7)
Strings on circles and T-duality
94(35)
Fields and strings on a circle
94(5)
The Kaluza--Klein reduction
95(1)
Closed strings on a circle
96(3)
T-duality for closed strings
99(1)
A special radius: enhanced gauge symmetry
100(3)
The circle partition function
103(1)
Toriodal compactifications
104(4)
More on enhanced gauge symmetry
108(5)
Lie algebras and groups
108(3)
The classical Lie algebras
111(2)
Physical realisations with vertex operators
113(1)
Another special radius: bosonisation
113(4)
String theory on an orbifold
117(2)
T-duality for open strings: D-branes
119(4)
Chan--Paton factors and Wilson lines
121(2)
D-brane collective coordinates
123(2)
T-duality for unoriented strings: orientifolds
125(4)
Background fields and world-volume actions
129(12)
T-duality in background fields
129(2)
A first look at the D-brane world-volume action
131(4)
World-volume actions from tilted D-branes
133(2)
The Dirac--Born--Infeld action
135(1)
The action of T-duality
136(1)
Non-Abelian extensions
136(2)
D-branes and gauge theory
138(1)
BPS lumps on the world-volume
138(3)
D-brane tension and boundary states
141(14)
The D-brane tension
142(6)
An open string partition function
142(3)
A background field computation
145(3)
The orientifold tension
148(2)
Another open string partition function
148(2)
The boundary state formalism
150(5)
Supersymmetric strings
155(37)
The three basic superstring theories
155(14)
Open superstrings: type I
155(5)
Closed superstrings: type II
160(5)
Type I from type IIB, the prototype orientifold
165(1)
The Green--Schwarz mechanism
166(3)
The two basic heterotic string theories
169(5)
SO(32) and E8 x E8 from self-dual lattices
171(1)
The massless spectrum
172(2)
The ten dimensional supergravities
174(2)
Heterotic toroidal compactifications
176(2)
Superstring toroidal compactification
178(1)
A superstring orbifold: discovering the K3 manifold
179(13)
The orbifold spectrum
180(3)
Another miraculous anomaly cancellation
183(1)
The K3 manifold
184(1)
Blowing up the orbifold
185(4)
Some other K3 orbifolds
189(2)
Anticipating D-manifolds
191(1)
Supersymmetric strings and T-duality
192(13)
T-duality of supersymmetric strings
192(3)
T-duality of type II superstrings
192(1)
T-duality of type I superstrings
193(1)
T-duality for the heterotic strings
194(1)
D-branes as BPS solitons
195(2)
The D-brane charge and tension
197(3)
The orientifold charge and tension
200(1)
Type I from type IIB, revisited
201(1)
Dirac charge quantisation
201(1)
D-branes in type I
202(3)
World-volume curvature couplings
205(19)
Tilted D-branes and branes within branes
205(1)
Anomalous gauge couplings
206(4)
Characteristic classes and invariant polynomials
210(6)
Anomalous curvature couplings
216(2)
A relation to anomalies
218(2)
D-branes and K-theory
220(1)
Further non-Abelian extensions
221(1)
Further curvature couplings
222(2)
The geometry of D-branes
224(25)
A look at black holes in four dimensions
224(14)
A brief study of the Einstein--Maxwell system
224(1)
Basic properties of Schwarzschild
225(3)
Basic properties of Reissner--Nordstrom
228(1)
Extremality, supersymmetry, and the BPS condition
228(4)
Multiple black holes and multicentre solutions
232(1)
Near horizon geometry and an infinite throat
233(1)
Cosmological constant; de Sitter and anti-de Sitter
233(1)
de-Sitter spacetime and the sphere
234(1)
Anti-de Sitter in various coordinate systems
235(1)
Anti-de Sitter as a hyperbolic slice
236(1)
Revisiting the extremal solution
237(1)
The geometry of D-branes
238(5)
A family of `p-brane' solutions
238(1)
The boost form of solution
239(1)
The extremal limit and coincident D-branes
240(3)
Probing p-brane geometry with Dp-branes
243(3)
Thought experiment: building p with Dp
243(1)
Effective Lagrangian from the world-volume action
244(1)
A metric on moduli space
245(1)
T-duality and supergravity solutions
246(3)
D(p + 1) from Dp
246(2)
D(p -- 1) from Dp
248(1)
Multiple D-branes and bound states
249(12)
Dp and Dp' from boundary conditions
249(3)
The BPS bound for the Dp--Dp' system
252(2)
Bound states of fundamental strings and D-strings
254(1)
The three-string junction
255(3)
Aspects of D-brane bound states
258(3)
0--0 bound states
258(1)
0--2 bound states
258(1)
0--4 bound states
259(1)
0--6 bound states
260(1)
0--8 bound states
260(1)
Strong coupling and string duality
261(21)
Type IIB/type IIB duality
261(3)
D1-brane collective coordinates
261(2)
S-duality and SL(2, Z)
263(1)
SO(32) Type I/heterotic duality
264(1)
D1-brane collective coordinates
264(1)
Dual branes from 10D string-string duality
265(6)
The heterotic NS-fivebrane
267(1)
The type IIA and type IIB NS5-brane
268(3)
Type IIA/M-theory duality
271(2)
A closer look at D0-branes
271(1)
Eleven dimensional supergravity
271(2)
E8 x E8 heterotic string/M-theory duality
273(3)
M2-branes and M5-branes
276(2)
Supergravity solutions
276(1)
From D-branes and NS5-branes to M-branes and back
277(1)
U-duality
278(4)
Type II strings on T5 and E6(6)
278(1)
U-duality and bound states
279(3)
D-branes and geometry I
282(40)
D-branes as probes of ALE spaces
282(9)
Basic setup and a quiver gauge theory
282(3)
The moduli space of vacua
285(1)
ALE space as metric on moduli space
286(3)
D-branes and the hyper-Kahler quotient
289(2)
Fractional D-branes and wrapped D-branes
291(3)
Fractional branes
291(1)
Wrapped branes
292(2)
Wrapped, fractional and stretched branes
294(6)
NS5-branes from ALE spaces
295(1)
Dual realisations of quivers
296(4)
D-branes as instantons
300(6)
Seeing the instanton with a probe
301(4)
Small instantons
305(1)
D-branes as monopoles
306(8)
Adjoint Higgs and monopoles
309(2)
BPS monopole solution from Nahm data
311(3)
The D-brane dielectric effect
314(8)
Non-Abelian world-volume interactions
314(2)
Stable fuzzy spherical D-branes
316(2)
Stable smooth spherical D-branes
318(4)
K3 orientifolds and compactification
322(23)
ZN orientifolds and Chan--Paton factors
322(2)
Loops and tadpoles for ALE ZM singularities
324(9)
One-loop diagrams and tadpoles
324(1)
Computing the one-loop diagrams
325(5)
Extracting the tadpoles
330(3)
Solving the tadpole equations
333(3)
T-duality relations
333(1)
Explicit solutions
334(2)
Closed string spectra
336(3)
Open string spectra
339(2)
Anomalies for N = 1 in six dimensions
341(4)
D-branes and geometry II
345(22)
Probing p with D(p -- 4)
345(1)
Probing six-branes: Kaluza--Klein monopoles and M-theory
346(2)
The moduli space of 3D supersymmetric gauge theory
348(4)
Wrapped branes and the enhancon mechanism
352(8)
Wrapping D6-branes
353(1)
The repulson geometry
354(2)
Probing with a wrapped D6-brane
356(4)
The consistency of excision in supergravity
360(2)
The moduli space of pure glue in 3D
362(5)
Multi-monopole moduli space
363(4)
Towards M- and F-theory
367(42)
The type IIB string and F-theory
367(27)
Sl(2, Z) duality
368(1)
The (p, q) strings
369(2)
String networks
371(2)
The self-duality of D3-branes
373(2)
(p, q) Fivebranes
375(1)
Sl(2, Z) and D7-branes
376(3)
Some algebraic geometry
379(4)
F-theory, and a dual heterotic description
383(1)
(p, q) Sevenbranes
384(2)
Enhanced gauge symmetry and singularities of K3
386(1)
F-theory at constant coupling
387(5)
The moduli space of N = 2 SU (N) with Nf = 4
392(2)
M-theory origins of F-theory
394(6)
M-branes and odd D-branes
396(3)
M-theory on K3 and heterotic on T3
399(1)
Type IIA on K3 and heterotic on T4
400(1)
Matrix theory
400(9)
Another look at D0-branes
401(1)
The infinite momentum frame
402(2)
Matrix string theory
404(5)
D-branes and black holes
409(31)
Black hole thermodynamics
409(5)
The path integral and the Euclidean calculus
409(2)
The semiclassical approximation
411(1)
The temperature of black holes
412(2)
The Euclidean action calculus
414(4)
The action for Schwarzschild
414(2)
The action for Reissner--Nordstrom
416(1)
The laws of thermodynamics
417(1)
D = 5 Reissner--Nordstrom black holes
418(11)
Making the black hole
420(5)
Microscopic entropy and a 2D field theory
425(2)
Non-extremality and a 2D dilute gas limit
427(2)
Near horizon geometry
429(3)
Replacing T4 with K3
432(8)
The geometry
432(1)
The microscopic entropy
433(1)
Probing the black hole with branes
434(3)
The enhancon and the second law
437(3)
D-branes, gravity and gauge theory
440(27)
The AdS/CFT correspondence
441(11)
Branes and the decoupling limit
441(2)
Sphere reduction and gauged supergravity
443(3)
Extracts from the dictionary
446(3)
The action, counterterms, and the stress tensor
449(3)
The correspondence at finite temperature
452(3)
Limits of the non-extremal D3-brane
452(1)
The AdS--Schwarzschild black hole in global coordinates
453(2)
The correspondence with a chemical potential
455(9)
Spinning D3-branes and charged AdS black holes
455(4)
The AdS--Reissner--Nordstrom black hole
459(1)
Thermodynamic phase structure
459(5)
The holographic principle
464(3)
The holographic renormalisation group
467(37)
Renormalisation group flows from gravity
467(5)
A BPS domain wall and supersymmetry
469(3)
Flowing on the Coulomb branch
472(8)
A five dimensional solution
472(3)
A ten dimensional solution
475(1)
Probing the geometry
475(3)
Brane distributions
478(2)
An N = 1 gauge dual RG flow
480(14)
The five dimensional solution
482(4)
The ten dimensional solution
486(1)
Probing with a D3-brane
487(1)
The Coulomb branch
488(1)
Kahler structure of the Coulomb branch
489(5)
An N = 2 gauge dual RG flow and the enhancon
494(8)
The five dimensional solution
494(4)
The ten dimensional solution
498(1)
Probing with a D3-brane
499(1)
The moduli space
500(2)
Beyond gravity duals
502(2)
Taking stock
504(6)
References 510(19)
Index 529


Clifford V. Johnson obtained his BSc in physics at Imperial College, University of London, and his PhD in theoretical physics from the University of Southampton. He is currently Senior Lecturer in Theoretical Physics, Department of Mathematical Sciences, University of Durham, where he is part of the Centre for Particle Theory.
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