請用此 Handle URI 來引用此文件：
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/43196完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 賀培銘(Pei-Ming Ho) | |
| dc.contributor.author | Ru-Chuen Hou | en |
| dc.contributor.author | 侯汝純 | zh_TW |
| dc.date.accessioned | 2021-06-15T01:42:01Z | - |
| dc.date.available | 2009-07-22 | |
| dc.date.copyright | 2009-07-22 | |
| dc.date.issued | 2009 | |
| dc.date.submitted | 2009-07-13 | |
| dc.identifier.citation | [1] J. Bagger and N. Lambert, Gauge Symmetry and Supersymmetry of Multiple M2-Branes,' Phys.
Rev. D 77, 065008 (2008) [arXiv:0711.0955 [hep-th]]. [2] J. Bagger and N. Lambert, Comments On Multiple M2-branes,' JHEP 0802, 105 (2008) [arXiv:0712.3738 [hep-th]]. [3] A. Gustavsson, Algebraic structures on parallel M2-branes,' arXiv:0709.1260 [hep-th]. [4] A. Gustavsson, Selfdual strings and loop space Nahm equations,' arXiv:0802.3456 [hep-th]. [5] J. Gomis, G. Milanesi, and J. G. Russo, Bagger-Lambert Theory for General Lie Algebras,' JHEP 06, 075 (2008) [arXiv:0805.1012 [hep-th]]. [6] S. Benvenuti, D. Rodriguez-Gmez, E. Tonni, and H. Verlinde, N=8 superconformal gauge theo- ries and M2 branes,' arXiv:0805.1087 [hep-th]. [7] P. M. Ho, Y. Imamura, and Y. Matsuo, M2 to D2 revisited,' JHEP 07, 003 (2008) [arXiv:0805.1202 [hep-th]]. [8] P. M. Ho and Y. Matsuo, A toy model of open membrane ‾eld theory in constant 3-form °ux,' Gen. Rel. Grav. 39, 913 (2007) [arXiv:hep-th/0701130]. [9] Y. Kawamura, Cubic matrix, generalized spin algebra and uncertainty relation,' Prog. Theor. Phys. 110, 579 (2003) [arXiv:hep-th/0304149]. [10] Y. Nambu, Generalized Hamiltonian dynamics,' Phys. Rev. D 7, 2405 (1973). [11] G. Papadopoulos, M2-branes, 3-Lie Algebras and Plucker relations,' arXiv:0804.2662 [hep-th]. [12] J. P. Gauntlett and J. B. Gutowski, Constraining Maximally Supersymmetric Membrane Ac- tions,' arXiv:0804.3078 [hep-th]. [13] R. WeitzenbÄok, Invariantentheorie,' P. Noordho®, GrÄoningen, 1923. Ph. Gautheron, Some re- marks concerning Nambu mechanics,' Lett. in Math. Phys. 37 (1996), 103. D. Alekseevsky, P. Guha, On Decomposability of Nambu-Poisson Tensor,' Acta. Math. Univ. Commenianae 65 (1996), 1. R. Ib¶anez, M. de Le¶on, J. C. Marrero, D. M. de Diego, Dynamics of generalized Poisson and Nambu-Poisson brackets,' J. of Math. Physics 38 (1997), 2332. N. Nakanishi, On Nambu-Poisson Manifolds,' Reviews in Mathematical Physics 10 (1998), 499. G. Marmo, G. Vilasi, A. M. Vinogradov, The local structure of n-Poisson and n-Jacobi manifolds,' J. Geom. Physics 25 (1998), 141. [14] B. de Wit, J. Hoppe and H. Nicolai, On the quantum mechanics of supermembranes,' Nucl. Phys. B 305, 545 (1988). [15] H. Aoki, N. Ishibashi, S. Iso, H. Kawai, Y. Kitazawa and T. Tada, Noncommutative Yang-Mills in IIB matrix model,' Nucl. Phys. B 565, 176 (2000) [arXiv:hep-th/9908141]. [16] J. Hoppe, On M-Algebras, the Quantisation of Nambu-Mechanics, and Volume Preserving Dif- feomorphisms,' Helv. Phys. Acta 70, 302 (1997) [arXiv:hep-th/9602020]. [17] S. Kawamoto and N. Sasakura, Open membranes in a constant C-‾eld background and noncom- mutative boundary strings,' JHEP 0007, 014 (2000) [arXiv:hep-th/0005123]. [18] Y. Matsuo and Y. Shibusa, Volume preserving di®eomorphism and noncommutative branes,' JHEP 0102, 006 (2001) [arXiv:hep-th/0010040]. [19] Y. Kawamura, Cubic matrix, Nambu mechanics and beyond,' Prog. Theor. Phys. 109, 153 (2003) [arXiv:hep-th/0207054]. [20] V. T. Filippov, 'n-Lie algebras,' Sib. Mat. Zh.,26, No. 6, 126140 (1985). [21] M. Schlesinger, J. D. Stashe®, The Lie algebra structure of tangent cohomology and deformation theory,' J. Pure Appl. Algebra 38 (1985), 313. P. Hanlon, M. L. Wachs, On Lie k-algebras,' Adv. in Math. 113 (1995), 206. J. A. Azc¶arraga, A. M. Perelomov, J. C. P¶erez Bueno, New generalized Poisson structures,' J. Phys. A29 (1996), 627. -ary Lie and associative algebras,' Redn. Sem. Math. Univ. Pol. Torino 53 (1996), 373. J. A. Azc¶arraga, J. M. Izquierdo, J. C. P¶erez Bueno, On the higher order generalizations of Poisson structures', J. Phys. A30 (1997), L607. R. Ib¶a~nez, M. de Le¶on, J. C. Marrero, D. Mart¶³n de Diego, Dynamics of generalized Poisson and Nambu-Poisson brackets,' J. Math. Phys. 38 (1997), 2332. P. W. Michor, A. M. Vinogradov, -ary Lie and associative algebras,' Rend. Sem. Mat. Torino, 53 (1996), 373. [22] T. Curtright and C. K. Zachos, Phys. Rev. D 68, 085001 (2003) [arXiv:hep-th/0212267]. [23] M. A. Bandres, A. E. Lipstein and J. H. Schwarz, N = 8 Superconformal Chern{Simons Theo- ries,' arXiv:0803.3242 [hep-th]. [24] L. Takhtajan, On Foundation Of The Generalized Nambu Mechanics (Second Version),' Com- mun. Math. Phys. 160, 295 (1994) [arXiv:hep-th/9301111]. [25] I. Vaisman, A survey on Nambu-Poisson brackets,' Acta. Math. Univ. Comenianae 2 (1999), 213. [26] J. -P. Dufour, N. T. Zung, Linearization of Nambu structures,' Compositio Mathematica 117 (1999), 83. [27] U. Gran, B. E. W. Nilsson and C. Petersson, On relating multiple M2 and D2-branes,' arXiv:0804.1784 [hep-th]. [28] H. Awata, M. Li, D. Minic and T. Yoneya, On the quantization of Nambu brackets,' JHEP 0102, 013 (2001) [arXiv:hep-th/9906248]. [29] J. Grabowski, G. Marmo, On Filippov algebroids and multiplicative Nambu-Poisson structures,' Di®. Geom. Appl. 12 (2000), 35. [30] Z. Guralnik and S. Ramgoolam, On the polarization of unstable D0-branes into non-commutative odd spheres,' JHEP 0102 (2001) 032 [arXiv:hep-th/0101001]. [31] I. R. Klebanov and A. A. Tseytlin, Entropy of Near-Extremal Black p-branes,' Nucl. Phys. B 475, 164 (1996) [arXiv:hep-th/9604089]. J. A. Harvey, R. Minasian and G. W. Moore, Non- abelian tensor-multiplet anomalies,' JHEP 9809, 004 (1998) [arXiv:hep-th/9808060]. M. Hen- ningson and K. Skenderis, The holographic Weyl anomaly,' JHEP 9807, 023 (1998) [arXiv:hep- th/9806087]. [32] K. M. Lee and H. U. Yee, BPS string webs in the 6-dim (2,0) theories,' JHEP 0703, 057 (2007) [arXiv:hep-th/0606150]. [33] A. Basu and J. A. Harvey, The M2-M5 brane system and a generalized Nahm's equation,' Nucl. Phys. B 713, 136 (2005) [arXiv:hep-th/0412310]. [34] D. S. Berman, L. C. Tadrowski and D. C. Thompson, Aspects of Multiple Membranes,' arXiv:0803.3611 [hep-th]. [35] S. Mukhi and C. Papageorgakis, M2 to D2,' arXiv:0803.3218 [hep-th]. [36] M. Van Raamsdonk, Comments on the Bagger-Lambert theory and multiple M2-branes,' arXiv:0803.3803 [hep-th]. [37] N. Lambert and D. Tong, Membranes on an Orbifold,' arXiv:0804.1114 [hep-th]. [38] J. Distler, S. Mukhi, C. Papageorgakis and M. Van Raamsdonk, M2-branes on M-folds,' arXiv:0804.1256 [hep-th]. [39] B. Pioline, Comments on the topological open membrane,' Phys. Rev. D 66, 025010 (2002) [arXiv:hep-th/0201257]. [40] J. Bagger and N. Lambert, Modeling multiple M2's,' arXiv:hep-th/0611108. [41] P.-M. Ho, Y. Matsuo, and S. Shiba, Lorentzian Lie (3)-algebra and toroidal compacti‾cation of M/string theory,' arXiv:hep-th/0901.2003. [42] Paul de Medeiros, Jos¶e Figueroa-O'Farrill, Elena M¶endez-Escobar and Patricia Ritter, Metric 3-Lie algebras for unitary Bagger-Lambert theories,' arXiv:hep-th/0902.4674. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/43196 | - |
| dc.description.abstract | We review the superconformal Lagrangian describing the low energy dynamics of multiple coinci-
dent M2 branes with Lie 3-algebra, and constructed some examples of Lie 3-algebra of ‾nite dimensions. The mathematical structures of Lie 3-algebra encode all the information of the theory. In order to understanding the properties of 11D M theory, and gaining some insight into the degrees of freedom of multiple M2-branes, we also developed the cubic matrix representation. This representation enables us to ‾nd an e®ective ‾eld theory in the large N limit. The fat graph structure and power counting for any Feynman diagram with arbitrary interacting vertices are available. Finally we also got the upper bound of power of N for any diagram with no external legs, but still can not see the N^(3/2) degrees of freedom in M theory. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-15T01:42:01Z (GMT). No. of bitstreams: 1 ntu-98-D91222002-1.pdf: 785307 bytes, checksum: 1dcbb3eb5a4d32d01ef9ed4fcebe8b0c (MD5) Previous issue date: 2009 | en |
| dc.description.tableofcontents | 1 Introduction 3
1.1 BLG Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Lie n-Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2.1 De‾nitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2.2 Review of Nambu-Poisson Brackets . . . . . . . . . . . . . . . . . . . . . . . . . 7 2 Mathematical Background on Lie 3-Algebra 10 2.1 Examples of Lie 3-Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.1.1 Linear Nambu-Poisson Bracket: Type I . . . . . . . . . . . . . . . . . . . . . . 10 2.1.2 Linear Nambu-Poisson Bracket: Type II . . . . . . . . . . . . . . . . . . . . . . 11 2.1.3 One-Generator Extension of a Lie Algebra . . . . . . . . . . . . . . . . . . . . . 11 2.1.4 A Truncation of Nambu-Poisson Structure on S3 . . . . . . . . . . . . . . . . . 12 2.1.5 An Extension of A4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.1.6 Truncation of a Nambu-Poisson Algebra . . . . . . . . . . . . . . . . . . . . . . 15 2.1.7 Level Extension of a 3-Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.1.8 A Conjecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.1.9 Comments on Lie 3-Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.2 Mathematical Discussion for Structure Constants fijkl . . . . . . . . . . . . . . . . . . 17 2.2.1 The Ansatz of the 3-Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.2.2 The Solutions of Fundamental identities . . . . . . . . . . . . . . . . . . . . . . 19 2.2.3 BLG model for Lorentzian 3-algebra with Jij ab 6= 0 only . . . . . . . . . . . . . . 20 2.3 Structure Theorem for Metric Lie 3-Algebras . . . . . . . . . . . . . . . . . . . . . . . 22 2.3.1 Metric Lie Algebras with maximally isotropic centre . . . . . . . . . . . . . . . 22 2.3.2 Metric Lie 3-Algebras with maximally isotropic centre . . . . . . . . . . . . . . 24 3 Application of Lie-3 Algebra via BLG model 27 3.1 Application of Lorentzian Lie-3 Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.1.1 From M2 to D2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.1.2 Dp to D(p + 1) via Kac-Moody algebra . . . . . . . . . . . . . . . . . . . . . . 29 3.2 M2 to M5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.2.1 Nambu-Poisson manifold and Lie 3-algebra . . . . . . . . . . . . . . . . . . . . 32 3.2.2 Rewriting ‾elds and covariant derivative . . . . . . . . . . . . . . . . . . . . . . 33 3.2.3 Action . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.2.4 Equivalence to M5-brane low energy theory . . . . . . . . . . . . . . . . . . . . 35 4 Application to Multiple M2-Branes 37 4.1 Basu-Harvey Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 4.2 Multiple M2-Brane Action . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 5 Cubic Matrix Representation 40 5.1 Representations of Nambu Bracket by Cubic Matrix . . . . . . . . . . . . . . . . . . . 40 5.1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 5.1.2 Realization by Cubic Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 5.1.3 Representations for A4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 5.1.4 Construction of Higher Representations . . . . . . . . . . . . . . . . . . . . . . 44 5.1.5 Comments on Irreducibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 5.2 Normal Cubic Matrices and Symmetry Transformations . . . . . . . . . . . . . . . . . 48 5.3 Relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 5.4 Cubic Matrix Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 5.4.1 Action . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 5.4.2 Feynman Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 5.5 Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 5.5.1 Large N Limit and Membrane . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 5.5.2 E®ective Field Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 5.5.3 Comments on Cubic Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 5.5.4 Some Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 Bibliography......................60 | |
| dc.language.iso | en | |
| dc.subject | 李三代數 | zh_TW |
| dc.subject | Lie 3-Algebra | en |
| dc.title | 李三代數與M膜 | zh_TW |
| dc.title | Lie 3-Algebra and M-branes | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 97-2 | |
| dc.description.degree | 博士 | |
| dc.contributor.oralexamcommittee | 高湧泉(Yeong-Chuan Kao),陳俊瑋(Jiunn-Wei Chen),高賢忠(Hsien-chung Kao),詹傳宗(Chuan-Tsung Chan) | |
| dc.subject.keyword | 李三代數, | zh_TW |
| dc.subject.keyword | Lie 3-Algebra, | en |
| dc.relation.page | 63 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2009-07-14 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 物理研究所 | zh_TW |
| 顯示於系所單位： | 物理學系 | |
文件中的檔案：
| 檔案 | 大小 | 格式 | |
|---|---|---|---|
| ntu-98-1.pdf 未授權公開取用 | 766.9 kB | Adobe PDF |
系統中的文件，除了特別指名其著作權條款之外，均受到著作權保護，並且保留所有的權利。