LEADER 07179nam 22007935 450 001 9910299970803321 005 20200629150859.0 010 $a4-431-54828-9 024 7 $a10.1007/978-4-431-54828-7 035 $a(CKB)3710000000143983 035 $a(EBL)1783678 035 $a(SSID)ssj0001276229 035 $a(PQKBManifestationID)11951253 035 $a(PQKBTitleCode)TC0001276229 035 $a(PQKBWorkID)11239448 035 $a(PQKB)10008740 035 $a(MiAaPQ)EBC1783678 035 $a(DE-He213)978-4-431-54828-7 035 $a(PPN)179765698 035 $a(EXLCZ)993710000000143983 100 $a20140630d2014 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aIntroduction to Supergravity /$fby Yoshiaki Tanii 205 $a1st ed. 2014. 210 1$aTokyo :$cSpringer Japan :$cImprint: Springer,$d2014. 215 $a1 online resource (134 p.) 225 1 $aSpringerBriefs in Mathematical Physics,$x2197-1757 ;$v1 300 $aDescription based upon print version of record. 311 $a1-322-17351-6 311 $a4-431-54827-0 320 $aIncludes bibliographical references at the end of each chapters and index. 327 $aPreface; Contents; 1 Introduction; 1.1 Supergravity and Superstring; 1.2 Gravitational Field; 1.2.1 Metric Formulation; 1.2.2 Vielbein Formulation; 1.3 Yang--Mills Field; 1.4 Antisymmetric Tensor Field; 1.4.1 Dual Field; 1.4.2 Self-dual Field; 1.4.3 Massive Chern--Simons Type Theory; References; 2 Supergravities in Four Dimensions; 2.1 Superalgebras and Supermultiplets; 2.2 Supersymmetric Field Theories; 2.3 mathcalN=1 Poincare? Supergravity; 2.4 Local Supersymmetry of mathcalN=1 Poincare? Supergravity; 2.4.1 Invariance of the Action; 2.4.2 Commutator Algebra 327 $a2.5 mathcalN=1 Anti de Sitter Supergravity2.6 Extended Supersymmetries; 2.7 mathcalN=2 Poincare? Supergravity; 2.8 mathcalN=2 Anti de Sitter Supergravity; 2.9 mathcalN 3 Supergravities; References; 3 Superalgebras and Supermultiplets; 3.1 Spinors in General Dimensions; 3.1.1 Gamma Matrices; 3.1.2 Dirac Spinors; 3.1.3 Weyl Spinors; 3.1.4 Majorana Spinors; 3.1.5 Majorana--Weyl Spinors; 3.1.6 Symplectic Majorana Spinors; 3.2 Super Poincare? Algebras; 3.3 Supermultiplets; 3.4 Massless Sectors of M Theory and Superstring Theory; 3.5 Super Anti de Sitter Algebras; References 327 $a4 Global Non-compact Symmetries4.1 Non-linear Sigma Models; 4.1.1 SL(2, mathbbR)/SO(2) Non-linear Sigma Model; 4.2 Duality Symmetry; 4.2.1 Duality Symmetry in General Even Dimensions; 4.2.2 Compact Duality Symmetry; 4.2.3 Non-compact Duality Symmetry; 4.3 D=4, mathcalN=8 Poincare? Supergravity; References; 5 Poincare? Supergravities in Higher Dimensions; 5.1 General Structure of Poincare? Supergravities; 5.2 D=11, mathcalN=1 Poincare? Supergravity; 5.3 D=10, mathcalN=(1,1) Poincare? Supergravity; 5.4 D=10, mathcalN=(2,0) Poincare? Supergravity; 5.5 D=10, mathcalN=(1,0) Poincare? Supergravity 327 $aReferences6 Dimensional Reductions; 6.1 Compactifications and Dimensional Reductions; 6.2 Dimensional Reductions of Field Theories; 6.2.1 Gravitational Field; 6.2.2 Yang--Mills Field; 6.2.3 Antisymmetric Tensor Field; 6.3 Dimensional Reductions of D=11, mathcalN=1 Supergravity; 6.3.1 D=10 Theory; 6.3.2 D=9 Theory; 6.3.3 D=8 Theory; 6.3.4 D=7 Theory; 6.3.5 D=6 Theory; 6.3.6 D=5 Theory; 6.3.7 D=4 Theory; 6.4 Dimensional Reductions of D=10, mathcalN=(2,0) Supergravity; 6.5 Dimensional Reductions of D=10, mathcalN=(1,0) Supergravity; References; 7 Gauged Supergravities 327 $a7.1 Gauged Supergravities and Massive Supergravities7.2 D=4, mathscrN=8 Gauged Supergravity; 7.3 Gauged Supergravities in Higher Dimensions; 7.3.1 D=7, mathscrN=4 Gauged Supergravity; 7.3.2 D=5, mathscrN=8 Gauged Supergravity; 7.4 D=10, mathscrN=(1,1) Massive Supergravity; References; Appendix A Notation and Conventions; Appendix B Formulae of Gamma Matrices; Index 330 $aThis book is a pedagogical introduction to supergravity, a gravitational field theory that includes supersymmetry (symmetry between bosons and fermions) and is a generalization of Einstein's general relativity. Supergravity provides a low-energy effective theory of superstring theory, which has attracted much attention as a candidate for the unified theory of fundamental particles, and it is a useful tool for studying non-perturbative properties of superstring theory such as D-branes and string duality. This work considers classical supergravities in four and higher spacetime dimensions with their applications to superstring theory in mind. More concretely, it discusses classical Lagrangians (or field equations) and symmetry properties of supergravities. Besides local symmetries, supergravities often have global non-compact symmetries, which play a crucial role in their applications to superstring theory. One of the main features of this book is its detailed discussion of these non-compact symmetries. The aim of the book is twofold. One is to explain the basic ideas of supergravity to those who are not familiar with it. Toward that end, the discussions are made both pedagogical and concrete by stating equations explicitly. The other is to collect relevant formulae in one place so as to be useful for applications to string theory. The subjects discussed in this book include the vielbein formulation of gravity, supergravities in four dimensions, possible types of spinors in various dimensions, superalgebras and supermultiplets, non-linear sigma models for non-compact Lie groups, electric-magnetic duality symmetries, supergravities in higher dimensions, dimensional reductions, and gauged and massive supergravities. 410 0$aSpringerBriefs in Mathematical Physics,$x2197-1757 ;$v1 606 $aMathematical physics 606 $aQuantum field theory 606 $aString models 606 $aGravitation 606 $aPhysics 606 $aMathematical Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/M35000 606 $aQuantum Field Theories, String Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/P19048 606 $aClassical and Quantum Gravitation, Relativity Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/P19070 606 $aMathematical Methods in Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19013 615 0$aMathematical physics. 615 0$aQuantum field theory. 615 0$aString models. 615 0$aGravitation. 615 0$aPhysics. 615 14$aMathematical Physics. 615 24$aQuantum Field Theories, String Theory. 615 24$aClassical and Quantum Gravitation, Relativity Theory. 615 24$aMathematical Methods in Physics. 676 $a530.1423 700 $aTanii$b Yoshiaki$4aut$4http://id.loc.gov/vocabulary/relators/aut$0721196 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910299970803321 996 $aIntroduction to supergravity$91410017 997 $aUNINA