請用此 Handle URI 來引用此文件：
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/46832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 | Chien-Ho Chen | en |
| dc.contributor.author | 陳建和 | zh_TW |
| dc.date.accessioned | 2021-06-15T05:41:58Z | - |
| dc.date.available | 2010-08-24 | |
| dc.date.copyright | 2010-08-24 | |
| dc.date.issued | 2010 | |
| dc.date.submitted | 2010-08-21 | |
| dc.identifier.citation | [1] M. Aganagic, J. Park, C. Popescu and J. H. Schwarz, “World-volume action of the M-theory …ve-brane,” Nucl. Phys. B 496, 191 (1997) [arXiv:hep-th/9701166].
[2] O. Aharony, O. Bergman, D. L. Ja¤eris and J. Maldacena, “N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals,”JHEP 0810, 091 (2008) [arXiv:0806.1218 [hep-th]]. [3] I. Y. Arefeva, D. M. Belov, A. A. Giryavets, A. S. Koshelev and P. B. Medvedev, “Noncommutative …eld theories and (super)string …field theories,” [arXiv:hep-th/0111208]. [4] T. Asakawa and I. Kishimoto, “Comments on gauge equivalence in noncommutative geometry,”JHEP 9911, 024 (1999) [arXiv:hep-th/9909139]. [5] P. Aschieri, C. Blohmann, M. Dimitrijevic, F. Meyer, P. Schupp and J. Wess, “A gravity theory on noncommutative spaces,” Class. Quant. Grav. 22, 3511 (2005) [arXiv:hep-th/0504183]. [6] P. Arvidsson, “Superconformal theories in six dimensions,” [arXiv:hep-th/0608014]. [7] J. Bagger and N. Lambert, “Modeling multiple M2’s,”Phys. Rev. D 75, 045020 (2007) [arXiv:hep-th/0611108]. [8] J. Bagger and N. Lambert, “Gauge Symmetry and Supersymmetry of Multiple M2-Branes,” Phys. Rev. D 77, 065008 (2008) [arXiv:0711.0955 [hep-th]]. [9] J. Bagger and N. Lambert, “Comments On Multiple M2-branes,”JHEP 0802, 105 (2008) [arXiv:0712.3738 [hep-th]]. [10] I. A. Bandos, K. Lechner, A. Nurmagambetov, P. Pasti, D. P. Sorokin and M. Tonin, “Covariant action for the super fi…ve-brane of M-theory,”Phys. Rev. Lett. 78, 4332 (1997) [arXiv:hep-th/9701149]. [11] 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]. [12] K. Becker, M. Becker and J. H. Schwarz, “String theory andM-theory: A modern introduction,”Cambridge, UK: Cambridge Univ. Pr. (2007) 739 p. [13] X. Bekaert, M. Henneaux and A. Sevrin, “Chiral forms and their deformations,”Commun. Math. Phys. 224, 683 (2001) [arXiv:hep-th/0004049]. [14] E. Bergshoe¤, E. Sezgin and P. K. Townsend, “Supermembranes and eleven-dimensional supergravity,”Phys. Lett. B 189, 75 (1987). [15] E. Bergshoe¤, 'The mathematical formulation of the M5-brane,' in Special Geometric Structures in String Theory, Bonn, 8th-11th Sept. 2001. [16] D. S. Berman, “M-theory branes and their interactions,”Phys. Rept. 456, 89 (2008) [arXiv:0710.1707 [hep-th]]. [17] M. Born and L. Infeld, “Foundations Of The New Field Theory,” Proc. Roy. Soc. Lond. A 144, 425 (1934). [18] C. G. . Callan, J. A. Harvey and A. Strominger, “World sheet approach to heterotic instantons and solitons,”Nucl. Phys. B 359, 611 (1991). [19] C. G. . Callan, J. A. Harvey and A. Strominger, “Worldbrane actions for string solitons,”Nucl. Phys. B 367, 60 (1991). [20] C. G. Callan and J. M. Maldacena, “Brane dynamics from the Born-Infeld action,”Nucl. Phys. B 513, 198 (1998) [arXiv:hep-th/9708147]. [21] A. Cannas da Silva, 'Lectures on symplectic geometry,' Lecture Notes in Mathematics, 1764. Springer-Verlag, Berlin, 2008 (corrected printing). [22] S. Cecotti, M. C. N. Cheng, J. J. Heckman and C. Vafa, “Yukawa Couplings in F-theory and Non-Commutative Geometry,” [arXiv:0910.0477 [hep-th]]. [23] C. H. Chen, P. M. Ho and T. Takimi, “A No-Go Theorem for M5-brane Theory,”JHEP 1003, 104 (2010) [arXiv:1001.3244 [hep-th]]. [24] C. H. Chen, K. Furuuchi, P. M. Ho, T. Takimi, “More on the Nambu-Poisson M5-brane theory: Scaling limit, background independence and an all order solution to the Seiberg-Witten map,”[arXiv:1006.5291 [hep-th]]. [25] C. S. Chu and P. M. Ho, “Noncommutative open string and D-brane,” Nucl. Phys. B 550, 151 (1999) [arXiv:hep-th/9812219]. [26] C. S. Chu and P. M. Ho, “Constrained quantization of open string in background B …eld and noncommutative D-brane,” Nucl. Phys. B 568, 447 (2000) [arXiv:hep-th/9906192]. [27] K. Dasgupta and S. Mukhi, “Orbifolds of M-theory,”Nucl. Phys. B 465, 399 (1996) [arXiv:hep-th/9512196]. [28] J. A. de Azcarraga, J. P. Gauntlett, J. M. Izquierdo and P. K. Townsend, “Topological Extensions of the Supersymmetry Algebra for Extended Objects,”Phys. Rev. Lett. 63, 2443 (1989). [29] J. A. de Azcarraga and J. M. Izquierdo, “n-ary algebras: a review with applications,” J. Phys. A 43, 293001 (2010) [arXiv:1005.1028 [math-ph]]. [30] B. de Wit, “Supergravity,” 2001 Les Houches Summer School “Unity of Fundamental Physics: Gravity, Gauge Theory and Strings,” [arXiv:hep-th/0212245]. [31] P. A. M. Dirac, “An Extensible model of the electron,” Proc. Roy. Soc. Lond. A 268 (1962) 57. [32] J. Distler, S. Mukhi, C. Papageorgakis and M. Van Raamsdonk, “M2-branes on M-folds,”JHEP 0805, 038 (2008) [arXiv:0804.1256 [hep-th]]. [33] M. R. Douglas, “Branes within branes,”[arXiv:hep-th/9512077]. [34] M. J. Du¤, P. S. Howe, T. Inami and K. S. Stelle, “Superstrings in D = 10 from supermembranes in D = 11,”Phys. Lett. B 191, 70 (1987). [35] M. J. Du¤ and K. S. Stelle, “Multi-membrane solutions of D = 11 supergravity,”Phys. Lett. B 253, 113 (1991). [36] J. P. Dufour, and N. T. Zung, “Poisson Structures and their normal forms,”Birkhäuser, 2005. [37] S. Fidanza, “Towards an explicit expression of the Seiberg-Witten map at all orders,”JHEP 0206, 016 (2002) [arXiv:hep-th/0112027]. [38] J. M. Figueroa-O’Farrill, “Three lectures on 3-algebras,”[arXiv:0812.2865 [hep-th]]. [39] V. T. Filippov, 'n-Lie algebras,' Sib. Mat. Zh.,26, (1985) 126-140 . [40] E. S. Fradkin and A. A. Tseytlin, “Nonlinear Electrodynamics From Quantized Strings,”Phys. Lett. B 163, 123 (1985). [41] J. P. Gauntlett, J. Gomis and P. K. Townsend, “BPS bounds for world-volume branes,”JHEP 9801, 003 (1998) [arXiv:hep-th/9711205]. [42] G. W. Gibbons, “Born-Infeld particles and Dirichlet p-branes,” Nucl. Phys. B 514, 603 (1998) [arXiv:hep-th/9709027]. [43] D. J. Gross and F. Wilczek, “Ultraviolet Behavior of Non-Abelian Gauge Theories,”Phys. Rev. Lett. 30, 1343 (1973). [44] R. Gueven, “Black p-brane solutions of D = 11 supergravity theory,”Phys. Lett. B 276 (1992) 49. [45] A. Gustavsson, “Algebraic structures on parallel M2-branes,”Nucl. Phys. B 811, 66 (2009) [arXiv:0709.1260 [hep-th]]. [46] A. Gustavsson, “M5 brane from mass deformed BLG theory,”JHEP 0911, 071 (2009) [arXiv:0909.2518 [hep-th]]. [47] A. Gustavsson, “An associative star-three-product and applications to M two/M …five-brane theory,”[arXiv:1008.0902 [hep-th]]. [48] P. M. Ho and Y. Matsuo, “M5 from M2,” JHEP 0806, 105 (2008) [arXiv:0804.3629 [hep-th]]. [49] P. M. Ho, “A Concise Review on M5-brane in Large C-Field Background,” [arXiv:0912.0445 [hep-th]]. [50] P. M. Ho, Y. Imamura and Y. Matsuo, “M2 to D2 revisited,”JHEP 0807, 003 (2008) [arXiv:0805.1202 [hep-th]]. [51] P. M. Ho, Y. Imamura, Y. Matsuo and S. Shiba, “M5-brane in three-form flux and multiple M2-branes,” JHEP 0808 (2008) 014 [arXiv:0805.2898 [hep-th]]. [52] G. T. Horowitz and A. Strominger, “Black strings and P-branes,” Nucl. Phys. B 360, 197 (1991). [53] P. S. Howe, N. D. Lambert and P. C. West, “The self-dual string soliton,” Nucl. Phys. B 515, 203 (1998) [arXiv:hep-th/9709014]. [54] P. S. Howe and R. W. Tucker, “A Locally Supersymmetric And Reparametrization Invariant Action For A Spinning Membrane,”J. Phys. A 10, L155 (1977). [55] C. M. Hull and P. K. Townsend, “Unity of superstring dualities,” Nucl. Phys. B 438, 109 (1995) [arXiv:hep-th/9410167]. [56] B. Jurco and P. Schupp, “Noncommutative Yang-Mills from equivalence of star products,”Eur. Phys. J. C 14, 367 (2000) [arXiv:hep-th/0001032]. [57] B. Jurco, P. Schupp and J.Wess, “Noncommutative gauge theory for Poisson manifolds ,”Nucl. Phys. B 584, 784 (2000) [arXiv:hep-th/0005005]. [58] B. Jurco, P. Schupp and J. Wess, “Nonabelian noncommutative gauge theory via noncommutative extra dimensions,” Nucl. Phys. B 604, 148 (2001) [arXiv:hep-th/0102129]. [59] B. Jurco, P. Schupp and J. Wess, “Noncommutative line bundle and Morita equivalence,” Lett. Math. Phys. 61, 171 (2002) [arXiv:hep-th/0106110]. [60] D. M. Kaplan and J. Michelson, “Zero Modes for the D=11 Membrane and Five-Brane,”Phys. Rev. D 53, 3474 (1996) [arXiv:hep-th/9510053]. [61] A. Kapustin, “Topological strings on noncommutative manifolds,”Int. J. Geom. Meth. Mod. Phys. 1, 49 (2004) [arXiv:hep-th/0310057]. [62] P. Koerber, “Abelian and non-Abelian D-brane e¤ective actions,”Fortsch. Phys. 52, 871 (2004) [arXiv:hep-th/0405227]. [63] E. Kiritsis, “String theory in a nutshell,”Princeton, USA: Univ. Pr. (2007) 588 p. [64] I. R. Klebanov and G. Torri, “M2-branes and AdS/CFT,” Int. J. Mod. Phys. A 25, 332 (2010) [arXiv:0909.1580 [hep-th]]. [65] N. Lambert and C. Papageorgakis, “Nonabelian (2,0) Tensor Multiplets and 3-algebras,”[arXiv:1007.2982 [hep-th]]. [66] N. Lambert and D. Tong, “Membranes on an Orbifold,”Phys. Rev. Lett. 101, 041602 (2008) [arXiv:0804.1114 [hep-th]]. [67] R. G. Leigh, “Dirac-Born-Infeld Action from Dirichlet Sigma Model,” Mod. Phys. Lett. A 4, 2767 (1989). [68] C. H. Liu and S. T. Yau, “D-branes and Azumaya noncommutative geometry: From Polchinski to Grothendieck,”[arXiv:1003.1178 [math.SG]]. [69] F. Lizzi, R. J. Szabo and A. Zampini, “Geometry of the gauge algebra in noncommutative Yang-Mills theory,”JHEP 0108, 032 (2001) [arXiv:hep-th/0107115]. [70] J. Madore, S. Schraml, P. Schupp and J. Wess, “Gauge theory on noncommutative spaces,”Eur. Phys. J. C 16, 161 (2000) [arXiv:hep-th/0001203]. [71] J. M. Maldacena, “The large N limit of superconformal …eld theories and supergravity,”Adv. Theor. Math. Phys. 2, 231 (1998) [Int. J. Theor. Phys. 38, 1113 (1999)] [arXiv:hep-th/9711200]. [72] A. Miemiec and I. Schnakenburg, “Basics of M-theory,” Fortsch. Phys.54, 5 (2006) [arXiv:hep-th/0509137]. [73] J. Moser,“ On the Volume Elements on a Manifold,”Transactions of the American Mathematical Society, 120(1965)286-294 [74] R. C. Myers, “Dielectric-branes,” JHEP 9912, 022 (1999) [arXiv:hep-th/9910053]. [75] K. Nagao, 'Non-commutative Donaldson-Thomas theory and vertex operators,' [arXiv:0910.5477 [math.AG]]. [76] W. Nahm, “A Simple Formalism For The Bps Monopole,”Phys. Lett. B 90, 413 (1980). [77] Y. Nambu, “Generalized Hamiltonian dynamics,” Phys. Rev. D 7, 2405 (1973). [78] T. Ortin, “Gravity And Strings,” Cambridge Unversity, Cambridge University Press, 2004. [79] P. Pasti, D. P. Sorokin and M. Tonin, “On Lorentz invariant actions for chiral p-forms,”Phys. Rev. D 55, 6292 (1997) [arXiv:hep-th/9611100]. [80] P. Pasti, D. P. Sorokin and M. Tonin, “Covariant action for a D = 11 five-brane with the chiral …eld,”Phys. Lett. B 398, 41 (1997) [arXiv:hep-th/9701037]. [81] P. Pasti, I. Samsonov, D. Sorokin and M. Tonin, “BLG-motivated Lagrangian formulation for the chiral two-form gauge …eld in D=6 and M5-branes,”Phys. Rev. D 80, 086008 (2009) [arXiv:0907.4596 [hep-th]]. [82] N. G. Pletnev, “Filippov-Nambu n-algebra relevant to physics,” Siberian Electronic Mathematical Reports 6(2009)272-311. [83] J. Polchinski, “Dirichlet-Branes and Ramond-Ramond Charges,” Phys. Rev. Lett. 75, 4724 (1995) [arXiv:hep-th/9510017]. [84] J. Polchinski, “String theory. Vol. 1: An introduction to the bosonic string, Vol. 2: Superstring theory and beyond. ” 1998,Cambridge, UK: Univ. Pr. [85] H. D. Politzer, “Reliable Perturbative Results for Strong Interactions?” Phys. Rev. Lett. 30, 1346 (1973). [86] A. M. Polyakov, “Quantum geometry of fermionic strings,”Phys. Lett. B103, 211 (1981). [87] J. Scherk and J. H. Schwarz, “Dual Models For Nonhadrons,”Nucl. Phys.B 81, 118 (1974). [88] J. H. Schwarz, “The M theory …five-brane,”arXiv:hep-th/9706197. [89] J. H. Schwarz, “Superconformal Chern-Simons theories,”JHEP 0411, 078 (2004) [arXiv:hep-th/0411077]. [90] N. Seiberg and E.Witten, “String theory and noncommutative geometry,” JHEP 9909 (1999) 032 [arXiv:hep-th/9908142]. [91] D. P. Sorokin and P. K. Townsend, “M-theory superalgebra from the M5-brane,”Phys. Lett. B 412, 265 (1997) [arXiv:hep-th/9708003]. [92] A. Strominger and C. Vafa, “Microscopic Origin of the Bekenstein-Hawking Entropy,”Phys. Lett. B 379, 99 (1996) [arXiv:hep-th/9601029]. [93] R. J. Szabo, “Quantum Field Theory on Noncommutative Spaces,”Phys. Rept. 378, 207 (2003) [arXiv:hep-th/0109162]. [94] B. Szendroi,'Non-commutative Donaldson-Thomas theory and the conifold,' Geom. Topol. 12 (2008) 1171-1202, [arXiv:0705.3419 [math.AG]]. [95] L. Takhtajan, “On Foundation Of The Generalized Nambu Mechanics (Second Version),” Commun. Math. Phys. 160, 295 (1994) [arXiv:hep-th/9301111]. [96] P. K. Townsend, “The eleven-dimensional supermembrane revisited,” Phys. Lett. B 350, 184 (1995) [arXiv:hep-th/9501068]. [97] P. K. Townsend, “D-branes from M-branes,”Phys. Lett. B 373, 68 (1996) [arXiv:hep-th/9512062]. [98] A. A. Tseytlin, “Born-Infeld action, supersymmetry and string theory,” [arXiv:hep-th/9908105]. [99] I. Vaisman, “Lectures on the Geometry of Poisson Manifolds,” Birkhäuser, 1994. [100] I. Vaisman, 'A survey on Nambu-Poisson brackets,' Acta Math. Univ. Comenian. 68 (1999) 213–241. [101] G. Veneziano, “Construction of a crossing-symmetric, Regge behaved amplitude for linearly rising trajectories,”Nuovo Cim. A 57, 190 (1968). [102] E. Witten, “Noncommutative Geometry And String Field Theory,”Nucl. Phys. B 268, 253 (1986). [103] E. Witten, “String theory dynamics in various dimensions,”Nucl. Phys. B 443, 85 (1995) [arXiv:hep-th/9503124]. [104] E. Witten, “Bound states of strings and p-branes,” Nucl. Phys. B 460, 335 (1996) [arXiv:hep-th/9510135]. [105] E. Witten, “Five-branes and M-theory on an orbifold,”Nucl. Phys. B 463,383 (1996) [arXiv:hep-th/9512219]. [106] E. Witten and D. I. Olive, “Supersymmetry Algebras That Include Topological Charges,”Phys. Lett. B 78, 97 (1978). [107] T. Yoneya, “Connection of Dual Models to Electrodynamics and Gravidynamics,”Prog. Theor. Phys. 51 (1974) 1907. [108] B. Zwiebach, “A …first course in string theory,”second edition, Cambridge, UK: Univ. Pr. (2009) 673 p. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/46832 | - |
| dc.description.abstract | M-theory is hoped to unify five superstring theories. In M-theory, there exists two fundamental extensive objects, M2- and M5-branes. They can relate to fundamental strings and D-branes by compactifying some directions of M-branes on a nontrivial submanifold. Recently, BLG model is proposed by manipulating Lie 3-algebra to construct multiple coincident M2-branes theory, which is a superconformal non-abelian gauge theory. Furthermore, manipulating a specific kind of Lie 3-algebra 'Nambu-Poisson bracket,' a single M5-brane theory is realized from the BLG M2-branes theory. Using double dimensional reduction, this theory can be reduced to the first order in coupling constant g of the noncommutative U(1) gauge theory on a D4-brane world-volume. But the Nambu-Poisson M5-brane theory cannot be deformed such that it reduces to the higher order terms of the Moyal bracket of the D4-brane theory. Therefore, we provide a no-go theorem describing that it is impossible to construct the higher order terms to match these two theories, at least perturbatively and in large C field background. A second order solution of Seiberg-Witten map of the theory is given, there appears an ambiguity for gauge transformation. An exact solution is also given without any free parameter. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-15T05:41:58Z (GMT). No. of bitstreams: 1 ntu-99-D93222002-1.pdf: 510966 bytes, checksum: 6a5be6e33e27bb06c157be356e227464 (MD5) Previous issue date: 2010 | en |
| dc.description.tableofcontents | 1 Introduction 3
1.1 Background and motivation . . . . . . . . . . . . . . 3 1.2 Recent developments . . . . . . . . . . . . . . . . . 4 2 String worldsheet and p-branes worldvolume theories and NCG 6 2.1 Polyakov world-sheet action of string . . . . . . . . 6 2.2 Nambu-Goto action of p-branes . . . . . . . . . . . . 8 2.3 Dirac-Born-Infeld and Wess-Zumino actions . . . . . . 9 2.4 D-brane and noncommutative geometry . . . . . . . . .12 3 BLG M2-brane worldvolume theory and Lie-3 algebra 16 3.1 A single M2-brane theory . . . . . . . . . . . . . . 16 3.2 Metric Lie 3-algebra . . . . . . . . . . . . . . . . 18 3.3 BLG multiple M2-branes theory . . . . . . . . . . . .19 4 M5-brane worldvolume theory 21 4.1 Pasti-Sorokin-Tonin M5-brane theory . . . . . . . . .22 4.2 Nambu-Poisson M5-brane theory . . . . . . . . . . . .23 4.2.1 Nambu-Poisson manifold . . . . . . . . . . . . . . 23 4.2.2 Nambu-Poisson 3-algebra . . . . . . . . . . . . . .24 4.2.3 M5 from M2 . . . . . . . . . . . . . . . . . . . . 24 4.2.4 Volume preserving diffeomorphism (VPD) . . . . . . 29 4.2.5 M5 to D4 . . . . . . . . . . . . . . . . . . . . . 30 4.3 No-go theorem . . . . . . . . . . . . . . . . . . . .34 4.4 Dimension analysis of Nambu-Poisson M5-brane theory 37 5 Seiberg-Witten map in the Nambu-Poisson M5-brane theory 39 5.1 The second order of the Seiberg-Witten map of b and κ41 5.2 The second order term of the Seiberg-Witten map B . .42 5.3 The origin of the e2 deformation: VPD . . . . . . . 44 5.4 An exact special solution of the Seiberg-Witten map 44 6 Conclusion 46 A Symplectic structure 48 B Poisson geometry 50 C Schouten-Nijenhuis bracket of multi-vector fields 51 Bibliography 53 | |
| dc.language.iso | en | |
| dc.title | 南部-泊松M5膜世界體理論及賽伯格威騰映射 | zh_TW |
| dc.title | Nambu-Poisson M5-brane world-volume theory and Seiberg-Witten map | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 98-2 | |
| dc.description.degree | 博士 | |
| dc.contributor.oralexamcommittee | 高涌泉,陳俊瑋,詹傳宗,高賢忠 | |
| dc.subject.keyword | M理論,超弦,膜動力學,賽伯格-威騰映射,非交換幾何, | zh_TW |
| dc.subject.keyword | M-theory,superstring,brane dynamics,Seiberg-Witten map,noncommutative geometry, | en |
| dc.relation.page | 59 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2010-08-21 | |
| 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-99-1.pdf 目前未授權公開取用 | 498.99 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。