國立虎尾科技大學 |

Classical mirror symmetry

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Classical mirror symmetry/ by Masao Jinzenji.
作者:	Jinzenji, Masao.
出版者:	Singapore :Springer Singapore : : 2018.,
面頁冊數:	viii, 140 p. :ill., digital ; : 24 cm.;
Contained By:	Springer eBooks
標題:	Mirror symmetry. -
電子資源:	http://dx.doi.org/10.1007/978-981-13-0056-1
ISBN:	9789811300561

Classical mirror symmetry
Jinzenji, Masao.

Classical mirror symmetry[electronic resource] /by Masao Jinzenji. - Singapore :Springer Singapore :2018. - viii, 140 p. :ill., digital ;24 cm. - SpringerBriefs in mathematical physics,v.292197-1757 ;. - SpringerBriefs in mathematical physics ;v.2..

1. Brief Introduction of Mirror Symmetry -- 2. Topological Sigma Models (A-Model and B-Model) -- 3. Basics of Geometry of Complex Manifolds -- 4. Detailed Computation of B-Model Prediction -- 5. Moduli space of Holomorphic Maps from CP^1 to CP^{N-1} -- 6. Localization Computation -- 7. Brief Outline of Direct Proof of Mirror Theorem.

This book furnishes a brief introduction to classical mirror symmetry, a term that denotes the process of computing Gromov-Witten invariants of a Calabi-Yau threefold by using the Picard-Fuchs differential equation of period integrals of its mirror Calabi-Yau threefold. The book concentrates on the best-known example, the quintic hypersurface in 4-dimensional projective space, and its mirror manifold. First, there is a brief review of the process of discovery of mirror symmetry and the striking result proposed in the celebrated paper by Candelas and his collaborators. Next, some elementary results of complex manifolds and Chern classes needed for study of mirror symmetry are explained. Then the topological sigma models, the A-model and the B-model, are introduced. The classical mirror symmetry hypothesis is explained as the equivalence between the correlation function of the A-model of a quintic hyper-surface and that of the B-model of its mirror manifold. On the B-model side, the process of construction of a pair of mirror Calabi-Yau threefold using toric geometry is briefly explained. Also given are detailed explanations of the derivation of the Picard-Fuchs differential equation of the period integrals and on the process of deriving the instanton expansion of the A-model Yukawa coupling based on the mirror symmetry hypothesis. On the A-model side, the moduli space of degree d quasimaps from CP^1 with two marked points to CP^4 is introduced, with reconstruction of the period integrals used in the B-model side as generating functions of the intersection numbers of the moduli space. Lastly, a mathematical justification for the process of the B-model computation from the point of view of the geometry of the moduli space of quasimaps is given. The style of description is between that of mathematics and physics, with the assumption that readers have standard graduate student backgrounds in both disciplines.

ISBN: 9789811300561

Standard No.: 10.1007/978-981-13-0056-1doiSubjects--Topical Terms:

591963
Mirror symmetry.

LC Class. No.: QC174.17.S9

Dewey Class. No.: 516.1

Classical mirror symmetry
LDR:03264nam a2200325 a 4500 001 925864
003 DE-He213
005 20180418133332.0
006 m d
007 cr nn 008maaau
008 190625s2018 si s 0 eng d
020 $a 9789811300561 $q (electronic bk.)
020 $a 9789811300554 $q (paper)
024 7 $a 10.1007/978-981-13-0056-1 $2 doi
035 $a 978-981-13-0056-1
040 $a GP $c GP
041 0 $a eng
050 4 $a QC174.17.S9
072 7 $a PHU $2 bicssc
072 7 $a SCI040000 $2 bisacsh
082 0 4 $a 516.1 $2 23
090 $a QC174.17.S9 $b J61 2018
100 1 $a Jinzenji, Masao. $3 1203934
245 1 0 $a Classical mirror symmetry $h [electronic resource] / $c by Masao Jinzenji.
260 $a Singapore : $c 2018. $b Springer Singapore : $b Imprint: Springer,
300 $a viii, 140 p. : $b ill., digital ; $c 24 cm.
490 1 $a SpringerBriefs in mathematical physics, $x 2197-1757 ; $v v.29
505 0 $a 1. Brief Introduction of Mirror Symmetry -- 2. Topological Sigma Models (A-Model and B-Model) -- 3. Basics of Geometry of Complex Manifolds -- 4. Detailed Computation of B-Model Prediction -- 5. Moduli space of Holomorphic Maps from CP^1 to CP^{N-1} -- 6. Localization Computation -- 7. Brief Outline of Direct Proof of Mirror Theorem.
520 $a This book furnishes a brief introduction to classical mirror symmetry, a term that denotes the process of computing Gromov-Witten invariants of a Calabi-Yau threefold by using the Picard-Fuchs differential equation of period integrals of its mirror Calabi-Yau threefold. The book concentrates on the best-known example, the quintic hypersurface in 4-dimensional projective space, and its mirror manifold. First, there is a brief review of the process of discovery of mirror symmetry and the striking result proposed in the celebrated paper by Candelas and his collaborators. Next, some elementary results of complex manifolds and Chern classes needed for study of mirror symmetry are explained. Then the topological sigma models, the A-model and the B-model, are introduced. The classical mirror symmetry hypothesis is explained as the equivalence between the correlation function of the A-model of a quintic hyper-surface and that of the B-model of its mirror manifold. On the B-model side, the process of construction of a pair of mirror Calabi-Yau threefold using toric geometry is briefly explained. Also given are detailed explanations of the derivation of the Picard-Fuchs differential equation of the period integrals and on the process of deriving the instanton expansion of the A-model Yukawa coupling based on the mirror symmetry hypothesis. On the A-model side, the moduli space of degree d quasimaps from CP^1 with two marked points to CP^4 is introduced, with reconstruction of the period integrals used in the B-model side as generating functions of the intersection numbers of the moduli space. Lastly, a mathematical justification for the process of the B-model computation from the point of view of the geometry of the moduli space of quasimaps is given. The style of description is between that of mathematics and physics, with the assumption that readers have standard graduate student backgrounds in both disciplines.
650 0 $a Mirror symmetry. $3 591963
650 1 4 $a Mathematics. $3 527692
650 2 4 $a Mathematical Physics. $3 786661
650 2 4 $a Quantum Field Theories, String Theory. $3 768973
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer eBooks
830 0 $a SpringerBriefs in mathematical physics ; $v v.2. $3 1062983
856 4 0 $u http://dx.doi.org/10.1007/978-981-13-0056-1
950 $a Mathematics and Statistics (Springer-11649)