Contributions Ã l'Etude du Vertex Topologique en ThÃ©orie ... - Toubkal

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013509-11 Refining the shifted topological vertex J. Math. Phys. 50, 013509 2009FIG. 2. A strict plane partition.For illustration, see the example Fig. 2... −1 0 1 ... A3 −2 = 3, −1 = 4,3, 0 = 5,3, 1 = 3,2, 2 = 2, 3 = 1.2. Property of Schur function for strict partitionThe shifted topological vertex is defined by using skew Schur P and Q functions. 20–22 Theseare symmetric functions that appear in topological amplitudes and are defined by a sequence ofpolynomials P x 1 ,x 2 ,...,x n , nN, with the property= P / x 1 , ...,x n Tx T , 0, otherwise, A4where the sum is over all shifted Young tableaux of shape /. The skew Schur function Q / isrelated to P / as in Eqs. 3.9 and 3.10. We also havestrict Q xP y = i,j1+x iy j1−x i y j.The relation between the Schur function P for strict partition that we have used here above andthe usual Schur functions S ˜ for the double partition ˜ is given byA5S ˜t =2 −l P 2t 2,A6where t/2 is t 1 /2,t 3 /2,t 5 /2,... and P t/2= P t 1 /2,t 3 /2,t 5 /2,.... Notice that the doublepartition ˜ in Frobenuis notation reads in terms of the strict partition =n 1 ,n 2 ,...,n k as˜ = n1 ,n 2 , ...,n k n 1 −1,n 2 −1, ...,n k−1 −1.A71 M. Aganagic, A. Klemm, M. Marino, and C. Vafa, Commun. Math. Phys. 254, 425 20052 A. Iqbal and A.-K. Kashani-Poor, Adv. Theor. Math. Phys. 7, 457 2004.3 A. Okounkov, N. Reshetikhin, and C. Vafa, Prog. Math., 244, 597 2006.4 L. B. Drissi, H. Jehjouh, and E. H. Saidi, Nucl. Phys. B to be published.5 T. Graber and E. Zaslow, e-print arXiv:hep-th/0109075.6 M. Aganagic, A. Klemm, and C. Vafa, Z. Naturforsch., A: Phys. Sci. 57, 12002.7 D. Karp, C. Liu, and M. Marino, Geom. Topol. 10, 1152006.8 A. Iqbal, C. Kozcaz, and C. Vafa, e-print arXiv:hep-th/0701156.Downloaded 24 Mar 2009 to 140.105.16.64. Redistribution subject to AIP license or copyright; see http://jmp.aip.org/jmp/copyright.jsp
013509-12 Drissi, Jehjouh, and Saidi J. Math. Phys. 50, 013509 20099 M. Taki, e-print arXiv:hep-th/0710.1776.10 P. Ginsparg, e-print arXiv:hep-th/9108028.11 N. A. Nekrasov, Adv. Theor. Math. Phys. 7, 8312004.12 N. Nekrasov and A. Okounkov, e-print arXiv:hep-th/0306238.13 S. Gukov, A. Iqbal, and C. Kozçaz, e-print arXiv:hep-th/07051508.14 L. B. Drissi, H. Jehjouh, and E. H. Saidi, Nucl. Phys. B 801, 316 2008.15 O. Foda and M. Wheeler, e-print arXiv:math-ph/0612018.16 E. Ramos and S. Stanciu, Nucl. Phys. B 427, 3381994.17 E. H. Saidi and M. B. Sedra, J. Math. Phys. 35, 3190 1994.18 E. H. Saidi, M. B. Sedra, and J. Zerouaoui, Class. Quantum Grav. 12, 1567 1995.19 H. N. Temperley, Proc. R. Soc. London, Ser. A 199, 361 1949.20 A. Y. Orlov, e-print arXiv:math-ph/0302011.21 M. Vuleti, e-print arXiv:math.Co/0707.0532.22 M. Vuleti, e-print arXiv:math-ph/0702068.23 J. J. Heckman and C. Vafa, e-print arXiv:hep-th/0610005.Downloaded 24 Mar 2009 to 140.105.16.64. Redistribution subject to AIP license or copyright; see http://jmp.aip.org/jmp/copyright.jsp
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UNIVERSITÉ MOHAMMED V - AGDALFACUL
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TABLE DES MATIÈRES3.3 Invariants t
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TABLE DES MATIÈRES8.2 Fonctions de
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Avant ProposCe travail à été eff
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Lab/UFR PHEUne thèse représente u
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10Lab/UFR PHE
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Contributions à l’Etude du Verte
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2.1 Généralités sur les variét
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2.2 Conifoldavec (y 1 , y 2 ) ≠ (
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2.2 Conifoldoù µ est un nombre co
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2.3 Variétés de CY toriquesFig. 2
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2.3 Variétés de CY toriquesEn gé
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2.3 Variétés de CY toriquessur L
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2.3 Variétés de CY toriquesz3z1z2
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2.3 Variétés de CY toriquesFig. 2
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du vertex U 3r α = |z 1 | 2 − |z
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3.1 Théorie des cordes topologique
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3.2 Dualité corde ouverte / corde
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3.3 Invariants topologiquesNotons a
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3.3 Invariants topologiquesoù F es
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3.3 Invariants topologiquesDans le
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3.3 Invariants topologiquesL’acti
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3.4 Modèle B et espace twistorielI
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H. Jehjouhprojectif complexe -PT d
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4.1 Variétés de CY toriques et cr
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Cela a fait apparaître d’autres
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4.2 Fonction de partition perpendic
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4.3 Version raffinée de la fonctio
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4.3 Version raffinée de la fonctio
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4.4 Modèle du cristal fondu et con
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4.4 Modèle du cristal fondu et con
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4.5 Invariants topologiques dans le
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4.6 Contribution : Generalized MacM
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L.B. Drissi et al. / Nuclear Physic
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(Γ + (z) = exp −i ∑ )1n z−n
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(∏ ∞(Υ − (q) = Ω − qk ))k
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5.1 Formalisme du Vertex topologiqu
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5.3 Vertex Topologique et Théorie
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H. JehjouhL’amplitude des produit
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176H. Jehjouh
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308 L.B. Drissi et al. / Nuclear Ph
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Page 215 and 216: Chapitre 6Vertex Topologique Raffin
Page 217 and 218: 5.1 Raffinement du vertex topologiq
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Page 225 and 226: 5.4 Vertex raffiné et homologie de
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Page 245 and 246: Conclusion et perspectivesde ce doc
Page 247 and 248: Fonctions de Schur et MacMahontopol
Page 249 and 250: Chapitre 8Annexe : Fonctions de Sch
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Page 277 and 278: Bibliographie[1] J. Polchinski, Str
Page 279 and 280: BIBLIOGRAPHIE[27] A.A. Belavin, A.
Page 281 and 282: BIBLIOGRAPHIE[57] A. Braverman and
Page 283 and 284: BIBLIOGRAPHIE[87] Yukiko Konishi, I
Page 285 and 286: BIBLIOGRAPHIE[119] D. A. Cox, The H
Page 287 and 288: BIBLIOGRAPHIE[150] C. Weiss and M.
Page 289 and 290: BIBLIOGRAPHIE[180] H. Awata and H.
Page 291: UNIVERSITÉ MOHAMMED V - AGDALFACUL
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Contributions Ã l'Etude du Vertex Topologique en ThÃ©orie ... - Toubkal

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