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N = 2 Supergravity in D = 4, 5, 6 Dimensions 2020 ed. [Minkštas viršelis]

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  • Formatas: Paperback / softback, 256 pages, aukštis x plotis: 235x155 mm, weight: 454 g, 126 Illustrations, black and white; XII, 256 p. 126 illus., 1 Paperback / softback
  • Serija: Lecture Notes in Physics 966
  • Išleidimo metai: 12-Mar-2020
  • Leidėjas: Springer Nature Switzerland AG
  • ISBN-10: 3030337553
  • ISBN-13: 9783030337551
Kitos knygos pagal šią temą:
N = 2 Supergravity in D = 4, 5, 6 Dimensions 2020 ed.Didesnis paveikslėlis
  • Formatas: Paperback / softback, 256 pages, aukštis x plotis: 235x155 mm, weight: 454 g, 126 Illustrations, black and white; XII, 256 p. 126 illus., 1 Paperback / softback
  • Serija: Lecture Notes in Physics 966
  • Išleidimo metai: 12-Mar-2020
  • Leidėjas: Springer Nature Switzerland AG
  • ISBN-10: 3030337553
  • ISBN-13: 9783030337551
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9783030337551.html
This graduate-level primer presents a tutorial introduction to and overview of N = 2 supergravity theories - with 8 real supercharges and in 4, 5 and 6 dimensions.

First, the construction of such theories by superconformal methods is explained in detail, and relevant special geometries are obtained and characterized.

Following, the relation between the supergravity theories in the various dimensions is discussed. This leads eventually to the concept of very special geometry and quaternionic-Kähler manifolds.

This concise text is a valuable resource for graduate students and young researchers wishing to enter the field quickly and efficiently.
1 Basic Ingredients
1(28)
1.1 Introduction
1(5)
1.2 Supersymmetric Theories with 8 Real Supercharges
6(18)
1.2.1 Multiplets
7(4)
1.2.2 The Strategy
11(1)
1.2.3 Rigid Conformal Symmetry
12(7)
1.2.4 Superconformal Groups
19(4)
1.2.5 Rigid Superconformal Symmetry
23(1)
References
24(5)
2 Gauging Spacetime Symmetries: The Weyl Multiplet
29(36)
2.1 Rules of (Super)Gauge Theories, Gauge Fields and Curvatures
29(2)
2.2 Gauge Theory of Spacetime Symmetries
31(7)
2.2.1 General Considerations
31(3)
2.2.2 Transformations of the Frame Fields
34(1)
2.2.3 Transformations of the Other Gauge Fields
35(3)
2.2.4 Transformations of Matter Fields
38(1)
2.3 Covariant Quantities and Covariant Derivatives
38(9)
2.3.1 Proof of Lemma on Covariant Derivatives
40(1)
2.3.2 Example: D = 6 Abelian Vector Multiplet
41(1)
2.3.3 Illustration of Full Calculation of the Transformation of a Curvature
42(2)
2.3.4 The Easy Way
44(2)
2.3.5 Non-closure Terms in D = 6 Abelian Vector Multiplet
46(1)
2.4 Curvature Constraints
47(4)
2.4.1 Constraint on R(P)
47(2)
2.4.2 Other Conventional Curvature Constraints
49(2)
2.5 Example: Non-SUSY Sigma Model
51(2)
2.6 The Standard Weyl Multiplets
53(10)
2.6.1 Matter Fields Completing the Weyl Multiplet
53(4)
2.6.2 D = 4
57(2)
2.6.3 D = 5
59(2)
2.6.4 D = 6
61(2)
References
63(2)
3 Matter Multiplets
65(46)
3.1 Review of the Strategy
66(1)
3.2 Conformal Properties of the Multiplets
67(26)
3.2.1 Vector Multiplets
69(4)
3.2.2 Intermezzo: Chiral Multiplet
73(4)
3.2.3 Rigid Hypermultiplets
77(13)
3.2.4 Hypermultiplets in Superconformal Gravity
90(2)
3.2.5 Tensor Multiplet in D = 4 Local Superconformal Case
92(1)
3.3 Construction of the Superconformal Actions
93(14)
3.3.1 Action for Vector Multiplets in D = 4
93(6)
3.3.2 Action for Vector Multiplets in D = 5
99(2)
3.3.3 Action for Hypermultiplets
101(6)
3.3.4 Splitting the Hypermultiplets and Example
107(1)
References
107(4)
4 Gauge Fixing of Superconformal Symmetries
111(48)
4.1 General Considerations
111(2)
4.2 Pure N = 2 Supergravity
113(7)
4.2.1 The Minimal Field Representation
113(3)
4.2.2 Version with Hypermultiplet Compensator
116(2)
4.2.3 Version with Tensor Multiplet Compensator
118(1)
4.2.4 Version with Nonlinear Multiplet Compensator
119(1)
4.3 Reduction from N = 2 to N = 1
120(5)
4.3.1 Reduction of the N = 2 Weyl Multiplet
121(2)
4.3.2 Reduction of the Compensating Vector Multiplet
123(1)
4.3.3 Reduction of the Second Compensating Multiplet
124(1)
4.4 Matter-Coupled Supergravity
125(9)
4.4.1 Elimination of Auxiliary Fields
126(2)
4.4.2 Gauge Fixing for Matter-Coupled Supergravity
128(2)
4.4.3 Full Action for D = 4
130(2)
4.4.4 Supersymmetry Transformations
132(2)
4.5 Vector Multiplet Scalars: Special Kahler Geometry
134(12)
4.5.1 Rigid Special Kahler Manifold
134(1)
4.5.2 Coordinates in the Projective Special Kahler Manifold
135(3)
4.5.3 The Kahler Potential
138(2)
4.5.4 Positivity Requirements
140(1)
4.5.5 Examples
141(1)
4.5.6 Kahler Reparameterizations
142(1)
4.5.7 The Kahler Covariant Derivatives
143(3)
4.6 Coordinates in the Quaternionic-Kahler Manifold
146(7)
4.6.1 Projective Coordinates
146(4)
4.6.2 S-Supersymmetry, Dilatations and SU(2) Gauge Fixing
150(1)
4.6.3 Isometries in the Projective Space
151(1)
4.6.4 Decomposition Rules
152(1)
4.7 D = 5 and D = 6, N = 2 Supergravities
153(2)
4.7.1 D = 5
153(1)
4.7.2 D = 6
154(1)
References
155(4)
5 Special Geometries
159(46)
5.1 D = 4, N = 2 Bosonic Action
160(1)
5.2 Symplectic Transformations
161(5)
5.2.1 Electric-Magnetic Dualities of Vector Fields in D = 4
161(2)
5.2.2 Symplectic Transformations in N = 2
163(3)
5.3 Characteristics of a Special Geometry
166(12)
5.3.1 Symplectic Formulation of the Projective Kahler Geometry
167(4)
5.3.2 Definitions
171(2)
5.3.3 Symplectic Equations and the Curvature Tensor
173(5)
5.4 Isometries and Symplectic Geometry
178(7)
5.4.1 Isometries of a Kahler Metric
178(4)
5.4.2 Isometries in Symplectic Formulation
182(1)
5.4.3 Gauged Isometries as Symplectic Transformations
183(2)
5.5 Electric-Magnetic Charges: Attractor Phenomenon
185(9)
5.5.1 The Spacetime Ansatz and an Effective Action
186(2)
5.5.2 Maxwell Equations and the Black Hole Potential
188(3)
5.5.3 Field Strengths and Charges
191(2)
5.5.4 Attractors
193(1)
5.6 Quaternionic-Kahler Manifolds
194(3)
5.6.1 Supersymmetry and Quaternionic Geometry
194(1)
5.6.2 Quaternionic Manifolds
195(1)
5.6.3 Quaternionic-Kahler Manifolds
196(1)
5.6.4 Quaternionic-Kahler Manifolds in Supergravity
196(1)
5.7 Relations Between Special Manifolds
197(3)
5.7.1 c-Map and r-Map
197(1)
5.7.2 Homogeneous and Symmetric Spaces
198(2)
References
200(5)
6 Final Results
205(28)
6.1 Final D = 4 Poincare Supergravity Results
205(19)
6.1.1 The Bosonic Action
208(4)
6.1.2 Physical Fermions
212(3)
6.1.3 The Fermionic Part of the Poincare Action
215(4)
6.1.4 Total Action
219(1)
6.1.5 Supersymmetry and Gauge Transformations
220(4)
6.2 Final Results for D = 5 Poincare Supergravity
224(4)
6.3 Final Remarks
228(1)
References
229(4)
A Notation
233(14)
A.1 Bosonic Part
233(3)
A.2 SU(2) Conventions
236(2)
A.2.1 Raising and Lowering Indices
236(1)
A.2.2 Triplets
237(1)
A.2.3 Transformations, Parameters and Gauge Fields
237(1)
A.3 Gamma Matrices and Spinors
238(6)
A.3.1 D = 4
239(1)
A.3.2 D = 5
240(1)
A.3.3 D = 6
241(1)
A.3.4 Products of y Matrices and Fierzing
242(2)
A.4 Spinors from 5 to 6 and 4 Dimensions
244(3)
B Superalgebras
247(8)
C Comparison of Notations
249(6)
References
251(4)
Index 255
Edoardo Lauria started his studies in Physics in Turin (Italy) and has concluded his Ph.D. at KU Leuven (Belgium) in 2018. His doctoral thesis has been published in the Springer Thesis series with the title Points, Lines, and Surfaces at Criticality. Currently, he holds a postdoctoral research position at Durham University and his research mainly focuses on conformal field theories.



Antoine Van Proeyen is professor emeritus at KU Leuven, Belgium. He started his research on supergravity in 1979, soon after his Ph.D. He has been involved in the construction of various supergravity theories, resulting special geometries, relations to string theory and applications to phenomenology and cosmology. He is co-author of the textbook 'Supergravity' with prof. Dan Freedman and he published 150 research papers with an h impact factor over 50.