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Results in Perturbative Quantum Supergravity from String Theory Piotr Tourkine

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Results in Perturbative Quantum Supergravity from String Theory Piotr Tourkine Results in perturbative quantum supergravity from string theory Piotr Tourkine To cite this version: Piotr Tourkine. Results in perturbative quantum supergravity from string theory. General Relativity and Quantum Cosmology [gr-qc]. Université Pierre et Marie Curie - Paris VI, 2014. English. NNT : 2014PA066295. tel-01165011 HAL Id: tel-01165011 https://tel.archives-ouvertes.fr/tel-01165011 Submitted on 18 Jun 2015 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. UNIVERSITE´ PIERRE ET MARIE CURIE - PARIS VI et INSTITUT DE PHYSIQUE THEORIQUE´ - CEA/SACLAY Ecole´ Doctorale de Physique de la R´egionParisienne - ED 107 Th`ese de doctorat Sp´ecialit´e: Physique Th´eorique Results in perturbative quantum supergravity from string theory. pr´esent´eepar Piotr Tourkine pour obtenir le grade de Docteur de l'Universit´ePierre et Marie Curie Th`esepr´epar´eesous la direction de Pierre Vanhove Soutenue le 09 juin 2014 devant le jury compos´ede: Zvi Bern Examinateur Emil Bjerrum-Bohr Examinateur (Membre invit´e) Michael Green Examinateur (Pr´esident du jury) Boris Pioline Examinateur David Skinner Rapporteur Dimitrios Tsimpis Rapporteur Pierre Vanhove Directeur de th`ese 1 2 A Anne-Marie, Marie-H´el`eneet Audrey, `aqui je dois tout. 3 4 Contents 1 Introduction 13 1.1 The UV question in quantum gravity. 13 1.2 Supergravities . 16 1.3 String theory . 19 2 The field theory limit of closed string amplitudes and tropical geometry 23 2.1 Closed string theory amplitudes and their field theory limit. 23 2.1.1 Superstring theory amplitudes . 23 2.1.2 The field theory limit. 26 2.2 A few words about tropical geometry and its link with classical geometry 28 2.2.1 Tropical geometry . 28 2.2.2 Classical geometry of Riemann surfaces . 32 2.2.3 From classical to tropical geometry . 34 2.3 Extraction of supergravity amplitudes . 41 2.3.1 Two-loops field theory limit in maximal supergravity . 42 2.3.2 New results at three loops . 43 3 Half-Maximal Supergravity 45 3.1 String theory models and their one-loop amplitudes. 45 3.1.1 CHL models in heterotic string . 49 3.1.2 Symmetric orbifolds of type II superstrings . 51 3.1.3 Worldline limit . 52 3.2 Two loops . 53 3.A Appendix on the one-loop divergence in D = 8 in CHL models . 58 3.A.1 Divergence in the non-analytic terms . 59 3.A.2 Divergence in the analytic terms . 59 4 BCJ double-copy in string theory 63 4.1 Review of the BCJ duality and double-copy. 64 4.2 Tree-level string theory understanding of BCJ . 66 4.3 Towards a string theoretic understanding in loop amplitudes . 71 4.3.1 BCJ ansatz for (N = 2) hyper multiplets. 72 4.3.2 String theoretic intuition . 72 4.3.3 Comparing the integrands . 74 5 Outlook 77 5 6 Personnal publications This manuscript is based on the first four publications and preprints [PT1, PT2, PT3, PT4] below. The content of [PT5] has not been covered in this text. [PT1] P. Tourkine and P. Vanhove, \An R4 non-renormalisation theorem in N = 4 supergravity," Class. Quant. Grav. 29, 115006 (2012) [arXiv:1202.3692 [hep-th]]. [PT2] P. Tourkine and P. Vanhove, \One-loop four-graviton amplitudes in N = 4 super- gravity models," Phys. Rev. D 87, no. 4, 045001 (2013) [arXiv:1208.1255 [hep-th]]. [PT3] P. Tourkine, \Tropical Amplitudes," arXiv:1309.3551 [hep-th]. [PT4] A. Ochirov and P. Tourkine, \BCJ duality and double copy in the closed string sector," JHEP 1405, 136 (2014) [arXiv:1312.1326 [hep-th]]. [PT5] N. E. J. Bjerrum-Bohr, P. H. Damgaard, P. Tourkine and P. Vanhove, \Scattering Equations and String Theory Amplitudes," arXiv:1403.4553 [hep-th]. 7 8 Remerciements En premier lieu je remercie chaudement David Skinner et Dimitrios Tsimpis pour m'avoir fait l'honneur d'^etrerapporteurs de ma th`ese.Je tiens ´egalement `aremercier les exami- nateurs qui se sont joints `aeux pour participer au jury : Zvi Bern, Emil Bjerrum-Bohr, Michael Green et Boris Pioline. Je suis tr`eshonor´ede l’effort qu'ils ont fourni pour con- cilier leurs emplois du temps afin d'^etretous pr´esents pour ma soutenance. Je souhaiterai aussi remercier plus g´en´eralement toutes les personnes ayant assist´eet m'encourager `a ma soutenance, dont certaines sont venues de bien loin. Concernant la soutenance, merci `al'IHES pour m'avoir aid´e`ar´esoudre l'inextricable en me laissant soutenir ma th`eseen ce lundi de Pentec^ote. Je remercie mon ensuite directeur de th`ese,Pierre Vanhove, qui m'a form´e`ala th´eorie des cordes et m'a fait profiter de son savoir. J'ai beaucoup appris de l'ensemble des discussions que nous avons pu avoir tout au long de cette th`ese.Je le remercie ´egalement de m'avoir encourag´e`aaller pr´esenter mes travaux en France et `al'´etrangerainsi que pour m'avoir permis d'assister `ade nombreuses ´ecoleset congr`es. Les chercheurs du labo aussi ont toujours ´et´ed'excellent conseil, scientifiques et autres, je souhaite parmi eux remercier tout particuli`erement Jean-Yves Ollitrault, Grisha Ko- rchemsky, Ruben Minasian, Iosif Bena, Bertrand Eynard, Mariana Grana et Sylvain Rib- ault. Quant au staff de l'IPhT, Sylvie Zafanella, Laure Sauboy, Anne Capdeon, Morgane Moulin, Anne Angles, Emmanuelle Delaborderie, Loic Bervas, Catherine Cathaldi, le staff info Laurent Sengmanivanh, Philippe Caresmel, Patrick Berthelot, Pascale Beurtey et son directeur Michel Bauer, votre efficacit´eet votre gentillesse `anulle autre pareille font vraiment de l'IPhT un endroit id´ealpour travailler. Au niveau scientifique, j'ai interagi avec de nombreuses personnes hors de l'IPhT pendant ma th`ese,je souhaite leur en porter cr´editici (de mani`ere d´esordonn´ee). Tout d'abord, les discussions que j'ai pu avoir avec Sam Grushevsky, commenc´eessur la plage de Carg`eseen 2012, m'ont beaucoup apport´e,entre autres par la d´ecouverte pour moi de la g´eom´etrietropicale dont une discussion ´etendueen rapport avec la physique est pr´esent´ee dans ce texte. A ce sujet je voudrais aussi remercier Ilia Itenberg et Erwan Brugall´e,pour leur gentillesse et leur patience lors des discussions que nous avons pu avoir. Ensuite, j'ai souvent pu interagir avec Guillaume Bossard au cours de mes ann´eesde th`ese,et j'ai toujours tir´egrand profit de ces discussions au sujet des th´eoriesde supergravit´eet des cordes. Je souhaiterais aussi remercier tout particuli`erement Oliver Schlotterer, pour toute l'aide qu'il m'a apport´eelors de mes s´ejoursau DAMTP et `al'AEI, mais aussi et surtout pour toutes les discussions scientifiques, sur les amplitudes en th´eoriedes cordes entre autres que nous avons pu avoir. Merci aussi `atoi Carlos pour ces discussions, j'esp`ere sinc`erement qu’`aCambridge je pourrai me joindre `avotre collaboration avec Oliver. Je remercie au passage ces instituts ainsi que l'institut Niels Bohr `aCopenhague pour leur 9 hospitalit´elors de mes s´ejoursl`a-bas.Je voudrais aussi remercier plus g´en´eralement les chercheurs avec qui j'ai pu discuter en divers endroits et diverses occasions, pour ces discussions et aussi pour certains pour leur soutien mat´eriel,dont Michael Green, Kelly Stelle, Emil Bjerrum Bohr, Massimo Bianchi, Marco Matone, Niklas Beisert, Stephan Stieberger, Francis Brown et Eric D'Hoker. Enfin, j'ai pu collaborer scientifiquement avec Alexandre Ochirov, et je voudrais le remercier d'avoir support´emon mauvais caract`ere pendant la fin de l'´ecrituresous pression du papier (m^emesi \objectivement" tu n'as pas non plus un bon caract`ere{ je plaisante). Je souhaiterais aussi sinc`erement remercier la RATP pour m'avoir aid´e`aapprofondir la signification du pr´eceptequi dit qu' \il y a du bon en tout". Une cons´equenceheureuse des quelques fois ou le RER n'a pas pu m'emmener `abon port `a´et´eque j'ai pu profiter de l'hospitalit´esympathique des th´esardsde Jussieu, Gautier, Thomas, Pierre, Demian, Thibault, Julius, Harold, Tresa, Luc et les autres, que je remercie. J'ai pu ainsi appr´ecier la qui´etudein´egalablequi r`egnedans ces bureaux, cons´equence, elle malheureuse,1 d'un choix de d'isolant thermique asbesteux il y a quelques 30 ann´eesde cela. Gautier, je souhaite tout particuli`erement te f´eliciter pour ta patience sans borne face `al'acharnement que j'ai pu mettre dans mes entreprises de d´econcentration multiples et r´ep´et´ees. Une cons´equencetout aussi des heureuse des autres fois o`ule RER a r´eussi`ame transporter `atravers Paris et la banlieue sud jusqu'au Guichet (quel nom bizarre) a ´et´e que j'ai pu profiter de la compagnie fort agr´eablede nombreuses g´en´erationsde th´esardsde l'IPhT, au sujet desquels je souhaite dire quelques mots maintenant, en commen¸cant par les anciens. Jean-Marie, H´el`ene, Emeline,´ Bruno, Gaetan, Gr´egoryet les autres, je vous dois en particulier mon habitude inlassable de vanner Alexandre, en plus de l'initiation `ala vie en th`ese`al'IPhT et la transmission du savoir imm´emorial des g´en´erationsde th´esardsayant exist´eavant nous sur terre.
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