Paper
0
One-loop Yukawa Couplings in Local Models
Authors
Joseph P. Conlon,Mark Goodsell
Eran Palti,Rui Filipe Pedreira Marques,Simaan AbouRizk,Ioannis Brilakis,Joanna Kapusta,Fabio Lopes Olivares,Olivier Ragueneau,Mitsugu Sohma,Eijun Itakura,sharad master,Daniella Schatz,Terry Carney,Marc Henneaux,Petr Levchenko,Aleksandra Skrabacz,Marcin Olszewski,Poul Damgaard,Ansgar Denner,Volodymyr Malyutenko,Leonardo Castellani,J. Luis Miramontes,Stephen Naculich,Carmelo P. Martin,Wilma Starke-Buzetti,Milagros Villasmil Molero,Assumpta Nnaggenda-Musana,Volker Adler,Stefan Scherer,Thomas Ferguson,Natalia Lazaretova,Diego P. Vázquez,Colin Bernet,Xinan Zhou,DIGAMBER PAWAR,Lorenz Eberhardt,Wael Haj Ahmad,Manuela Kulaxizi,Srinivasan Jagannathan,Lawrence Kennedy,Aurelien Bigot,Maria Sazanova,Alexander Haupt,Saleh Hamdan,Peter Wolfsteiner,Kosta Nikolić,Kristian Jensen,Bharat Char,Garrett Poe,Jelena Nikolić,Laura Ledesma,David Shih,Alain Jaccard,Carolyn Dzierba,Michael Johnson,Francesco Cilurzo,Marc Torrens,Benjamin Bellenie,Simone Giacomelli,Geofrey De Visscher,Andy Van Brocklin,Luis Garcés-Erice,Jing Shu,Seok Ki Choi,Robert Stala,Shulamit Levenberg,Gianluca Calcagni,Vishnu Ram OV,Jonathan Wall,José Tormos,Jose Endrino,Marie Connett,Bulent Basol,Pablo Montoya,Lorenzo Tancredi,Thorsten Alexander Kern,Christopher Herzog,Harri Mäkinen,Wai-Ching Lam,Martin Köhne,Claudia de Rham,David Clarke,Andre Lukas,Andrew Prokhorenkov,Josep D. Asis,Dan Andersen,Sónia Vladimira Correia,Nasuf SONMEZ,Fabio Maltoni,Martin Ward,Torsten Dahms,Jukka Suhonen,Martín Aluja,Dmitry Golubkov,M.M. Sheikh-Jabbari,Pol Bordas,Ada Campione,Valentin Geisler-Knünz,Li Ju,Aysel Kayis Topaksu,Esther Chávez-Miranda,Christopher Schadt,Jonathon Lookadoo,Hüseyin Bahtiyar,Rachel Bartek,Lothar Spiess,Paul Barrette,Leigh Gibson,John Hawdon,GIOVANNI SOTGIU,Kamila Kuros-Kowalska,Curt Sigmund,Parinya Karndumri,Eduardo Garcia-Valdecasas Tenreiro,Matthias Kaminski,SangHyun Lee,Andrei Parnachev,Dimitrios Lykomitros,Ahmet Umar,Neil Switz,Congkao Wen,Byron Wicks,Kavithaa Loganathan,Aninda Sinha,Tammy Ivins,Ingo Jordan,Nilanjan Brahma,Carlos Tamarit,Engel Roza,Paul Garrett,Sérgio Henrique Staut Brunini,Karin Bjerre,Andreja Istenic Starcic,Aleksi Vuorinen,Boris Pioline,Stefan Kallweit,Suprabh Prakash,Nuno Brandão,José María Pérez Collados,Cristina Albuquerque,Ezequiel Alvarez,Iosif Bena,Sai Putcha,Robert LoGalbo,Rong-Chi ,Stephane Coulombe,María de la Luz Casas-Perez,Matthias Gaberdiel,Vojtech Janousek,Christoph Stein,James Wetterer,Clara Cruz Santos,Brian Palik,Francesco Giordano,Gert Aarts,Gianluca Giavitto,Pierre Boudry,María-José Carrasco,Xian-Hui Ge,Arantza Oyanguren,Jeremy Dalseno,Andrew Frey,Oscar Vives,Timothy Hollowood,Simone Stracka,Nausheen Shah,Yu-Xiao Liu,Luc Demortier,Cheng-Wei Chiang,Walter Tangarife,Nicolas Neill,Peter Adshead,Tim Tait,Maurizio Martinelli,Choong Sun Kim,Iosif Breido,Ronnie Machielsen,Chan Youn Park,Connor Doak,Clara Amorim,Gabriele Travaglini,Young-Kyun Kwon,Andreas Brandhuber,Daniel O'Keefe,Jose Maria Alunda,Bin Wang,Niko Jokela,Stephen Wolfe,HIND ALKATAN,Sergio M. Ovruski,Jeppe Læssøe,David Lindsay,Juan Antonio Martínez Berbel,Dimitar Kanev,Allen Norrbom,Mark Pesaresi,Eduardo Gabriel Virla,Victor Manuel Vidal-Martinez,Salvatore My,Andreas Pfeiffer,Xavier Janssen,Junghwan Goh,Bruno Notteboom,Oktay Doğangün,Erhan Gülmez,Stan Boutin,Piet Verwilligen,Josep Flix,Georgios Papathanasiou,isabel mendez,Wei Song,Andre Lessa,Gerhard Kresbach,Sharlene Sing,Joseph Conlon,José María Viader-Salvadó,Lara Lloret Iglesias,Elena Bichenkova,Jorge Eduardo Pinto da Silva e Conceicao Santos,Tomohiko Hojo,José Miguel Figueroa-O'Farrill,Leonardo Giusti,Warren McNabb,Gonzalo Merino,Will Costain,Stephen Matthews,Agustín Estrada Peña,sandrine ,Emilio Meschi,stefano bianco,DANUTA PLUTA-WOJCIECHOWSKA,Nihan KATIRCI,Hannes Jung,Ruifu Yang,Jose Miguel Martinez Zapater,Margarita Samudio,Sami Maalej,Maksym Yasinskyy,Silke Fürst,Iwao Yamaguchi,Steve Paterson,KAI-FENG CHEN,Dimitrios Giataganas,William Tom,Miguel-Angel Monjas,Leo Wiggers,Stefano Ragazzi,Sven Schewe,Natale Demaria,Ching-Cheng Hsu,Igor Oya,Raquel de los Reyes Lopez,Paulo Granjo,Brian Markham,Yuri Andreev,Periklis Pantazis,Yang Zhang,Rami Najjar,Borun Chowdhury,Joao Varela,PRADIPTA GHOSH,Phillip Stanley-Marbell,Lorenzo Di Pietro,Jan Troost,Raul Arias,Andreas Braun,Carlos Hoyos Badajoz,Anna Maj,Rachelle Irwin,jing li,Fabio Zwirner,Daniel Grumiller,Mick Mulder,Hamid Reza Afshar,Wolfgang Dick,Maria Concepcion Gonzalez Garcia,PIETRO ALEARDO SICILIANO,Pietro Siciliano,Felipe Attanasio,Eugeen Vanmechelen,Peter Lutz,Davide Pagani,Chelcy Miniat,Antoni Szczuciński,Christopher Sears,Christiane Hudon,Bernd Scholz-Reiter,Boguslaw Pisarek,Thomas Van Riet,Gang Yang,Miguel Nebot Gómez,Matteo Beccaria,Leonardo Di Matteo,Xin Gao,Joanne Cole,Gurpreet Singh Chahal,Junjie Rao,Masanori Hanada,Stefano Pozzorini,Piergiulio Lenzi,Alessio Ghezzi,Darko Mekterović,Juan Eduardo Ramirez,Burak Bilki,Mauricio Sturla,Wojciech Dominik,Antonio Branca,Christian Saemann,Igor Goncharenko,智慧 王,Tomasz Stebel,Gianluca Grignani,Cem Eroncel,Evelina Gersabeck,Johannes Albrecht,KHELIFA ADEL,Jacco de Vries,Kenan Sogut,Andrea Davide Benaglia,Alexander Rudenko,Jairo Javier Martínez Montoya,Massimiliano Fiorini,Gabriele Rigo,Marc Baarmand,Gouranga Kole,Rodrigo Salgado,ali fahim,Vladimir Korenkov,Irina Nasteva,Victor Kim,Marco Grassi,Sergei Shmatov,Venelin Kozhuharov,Maria Almeida,Eduardo Picatoste,Alison Tully,LAURA AMBROSINI,Jaap Velthuis,Pedro Antoranz,Nikola Godinovic,Graeme Attwood,Henderik A. Proper,valerie VERDIER,Grigorii Konson,ANA OLEAGA,Nuria Oliver,Sambit Kumar Dash,Gregory Brown,Arto Mustajoki,Marta Hernandez,David Rodriguez-Lazaro,Maria Jesus Pacho,Armanda Matos,Mariana Grana,Mylène Pezet,Michele Maltoni,Javier Ibáñez,Yoh-ichi Tagawa,Werner Telesko,Venkataraman Subramanian,Ajith Ananthakrishna Pillai,Jaroslaw Wiechczynski,Thomas Schaefer,Hana Sychrova,Anna Rodkina,ERIC CHEN-HUA YU,Vadim Kramar,WAN-CHEN CHEN,CHING-HSIN YU,Wilson Rogério Penteado Júnior,Anja-Kristina Techen,Fátima Jorge,Marcel Hürlimann,Jill Johnstone,Elżbieta Szczygieł,John Hoxmeier,Enriqueta R. López,Johannes G. Mayer,Júlio Baima,Marian Lazar,Theresa Ochoa,Josefa Fernandez,Hideo Fujita,angela maria volpicella,Wout Broere,Wolfgang Rist,Emma Anhyela Guantay,Dimitrios Loukidis,Daniel Le Heron,ALP AYDINALP,Konstantinos Roumpedakis,Elizabeth Wood,Piotr Surowka,Yolanda Loarce,Mohammed Zidan,Albion Lawrence,Bin Wu,Jeremy Fried,Craig Mundy,Anja Schienkiewitz,Milko Palangurski,Arpan Bhattacharyya,Fabrizio Caola,Dario Livio Menasce,Andreas Recknagel,Alfonso Serrano-Maillo,María Rebeca Padilla de la Torre,Hyun Seok Yang,Ivan Gadjev,Renato Barcellos Rédua,Bohdan Serdenko,Pascal Tremblay,Nicolás Grandi,Jessica Scott,Krishna Seshadri,Malo Edi,Nima Afkhami-Jeddi,Patrick De Clercq,Brian Schwartz,JURACY PACÍIFCO,Kem Rogers,Agnieszka Czejkowska,Takahito OHMURA,Igor Bandos,Sebastian Mizera,Radek Malinský,Robert Ciesielski,Israel Belfer,N/A ,Gonçalo Cruz ,Sandro Ventura,Andreas Oehler,Balint Radics,Kazuki Takashima,Takaaki MANABE,Sergii Levich,R Donald Harvey,Ana Marta Ferreira,Jose Maldonado Escribano,Newton Lupwayi,Batoul Khalifa,John Lawrence,Anna Clara Bova,john Snape,Md Rajibul Karim,Katja Lembke,Elina Maslo,Michaela Bosakova,Annie J. Kuan,Miguel Bustos Rubio,Pierre Delage,Aureliano Ortega,James Rafferty,Maria da Felicidade Araújo Morais,Svetla Boytcheva,Tânia Vicente,Dori Cabrera,Stanislav Poslavsky,Sam Brown,Elnur Sadykhov,Tsutomu Fujimura,Xiaoran Zhao,Nadia Tonello,Charles Richardson,Pieter Taels,Alexandra Leitao-BenHamadou,Elżbieta Buchcic,Luis Manuel Ferreira Gomes,John Vogel,Nick Bond,Jenni Elina Mölkänen,Silvia Miksch,Benjamin Rosenthal,Giacomo ORTONA,Sebastian Waeber,Joaquim Llisterri,Nan Hatch,CHIA-RUNG LU,Flemming Ravn Merkel,Gerardo Pérez-Ponce de León,Juliana da Silva Pereira Andriani,Andrea Quadri,Roman Pyshkin,Luis Ángel Ballesteros Moffa,Wataru Fujii,Jesús Gerardo Martínez del Castillo,Koji Sugiura,Scott Koslow,Antonio Martín,Pao T. Kao,Markus Billeter,Jamie McMinn,Boris Napreev,Sławomira Kamińska-Berezowska,Gillian Owen Moreira,Mario Caneva Moutinho,Gisela Gonçalves,Pietro Longhi,Paulino Silva,Mohamad Forouzanfar,Marina Fernández Toirán,Vishal Anand,Sandra Gordon,Ulises Diéguez-Aranda,shailaja kheni,Mark Bocko,Grant Remmen,Louise Kuchel,Marcela Buchtova,Katarína Minarovičová,Boris Feshin,Howard Kaufman,Giacomo Sguazzoni,Alessia Rita Tricomi,Tommaso Boccali,Christina Gao,Emir Bozkurt,Amir Etemad-Shahidi,Umberto Amato,María del Rosario Cota-Yañez,Darren Gröcke,Marluci Menezes,Dolors Verdaguer,Callum Brodie,Joana Viana,Sahand Seifnashri,Dongxing Cao,Attila Karsi,Evaristo C. Martínez-Radío,Teresa Albuquerque,Mariola Wierzbicka,Jürgen Plöhn,Sojan Lal P,Artur Barreiros,Sushil Jain,Rita Castilho,Cristina E Carnovale,Dr.Dornadula Sundar Ram,Stavroula Kontoe,Fedor Ratnikov,Luigi Benussi,Vincenzo GALATA',Farhang Daneshmand,Jun-Hui Zheng,Dr. Hirsch Angelika B.,Ahmet Kurunc,Maciej Bilek,David Hodgson,gily coene,EDER SOMOZA VALDEOLMILLOS,Simonetta Capone,Nicolas Jouve,Isabel Margarida antunes,Anton Setzer,Andrew Lac,Benjamin Jaeger,Min-Kyu Paek,Veronique Feipel,Jeffrey Peakall,John MacKay,Katarzyna Węsierska,Jean-Francois Guégan,Kaltham Al-Ghanim,Luigi Lo Iacono,Takafumi Tsuboi,Farhat Afrin,Nobuo Nakada,Silvia Barona Vilar,Jacinto Serrão,Frederic THOMAS,Anabela Afonso,Toshihiro Tsuchiyama,Christa Tobler,Juan Antonio Balbuena,Chi-leung Hui,Maria JP Comuñas,Walter M. Jaklitsch,Antoine BAYLAUCQ,Erika Mayumi Watanabe,Weronika Wolszczak,Xiying Hao,Susanne Feist-Burkhardt,Lourenzo Fernández-Prieto,Hans-Jörg Schulz,Justin B. Runyon,Sergey Khitrin,Gabor M. Kovacs,Jean-Philippe Lansberg,Marco Diogo Richter Gomes da Silva,Walid Bennabi,Margarida Santos-Reis,Bruno Brunetti,Sergey Vernov,Krishnan Rama,Barbara Krumay,FILIPPOS ARAVANOPOULOS,mahmoud mohamed,Sean Stotyn,Maja Lundemark Andersen,Diana Mateus,Paulina Mata,Vladimir Myazin,Maria Costa,Jeongkil Park,Thomas Near,Patricia Ramírez Noguera,Sacha Mignon,Randip Bindra,Lore Decoster,Bernd Gröben,Carlos Teixeira,Daniel Viete,Christophe Roux,Henning Höfener,Kei Nakajima,Fernando Carrillo-Navarrete,MÁRCIO LUÍS COSTA,Pei-Yoong Lam,Aleksey Kostenko,Susan Eggly,Rolf Kemmler,Petra Kudejova,Benito Regueiro,Masao Watanabe,Grant Pierce,Jürgen Vogt,Henn Ojaveer,Daniel Mazin,GIANLUCA MARUCCI,Chunlei Su,Sabina Gałka,Rob W.. van Nues,Rafael Álvarez,Xavier De Bolle,Sabino Maggi,HIROYUKI KAWACHI,Raul Iglesias,Isak Davids,GIANMAURO FONTANA,Jesse Jenkins,Harald Hampel,Colin Moran,Nathalia Finck,守正 曾,Joerg Hermann,Huajun Jin,Kwang-Huei Lin,Peter Haeussler,Lina Quesada-Ocampo,Brittan Barker,Ivan Jesus Martinez Soler,Henry Vanderploeg,Ulf G Lundberg,Judite Primo,Nicolas TROQUARD,Lara Sidoli,Marija Colic,Thomas Unold,Rita Cadima,GÜLSEN ÇAYIR,Rakovec-Felser Zlatka,Giovanni Pelliccioli,Nelly Cecilia Alba de Sánchez,Juan de Jesús Galindo Niño,MARTINEZ-FERNANDEZ VALENTÍN-ALEJANDRO,Zhou Guoliang,Juan Pedro Henández Touset,Belinda Flem,Lenka Vondrovicová,S. Shajidul Haque,Steven Pells,David Levesque,Galina Parshina,Zalika Klemenc-Ketis,Federico Ibarra,Mai Minoura,Erickson Fajiculay,Hannah Turner,Joaquim Assunção,Christoph-Peter Strehl,Radu Grigore,Matthew Brousil,Elnaz Neinavaz,Michael Lee,Alejandro Londoño-Burbano,Marcondes Souza,Aravindhan Selvaraj,Jessie Galasso-Carbonnel,Heidi Siller,Oscar Juanatey-Boga,Jeryl English,Saraí Brito Cardoso,Mauricio Brunetto,Markus Garbiso,Veronica Oliveros,Lucíola Galvão Gondim Corrêa Feitosa,Alma Rosa Altúzar Molina,Ирина Тараскина,Claudia Albrecht,Elizabeth Ashley,Chantal Bassett,Gonzalo Guevara,Christian Creixell,Ricardo Cruz,Viviana Yánez-Mendizábal,tijen üner,Isabelle de Baptista,Qin ,Md Atiqur Rahman Sarker,Nicholas Ray,Laura DEGASPARE MONTE MASCARO,Erica Modesto,Vanessa Gomes da Silva,Philip-Neri Jayson-Quashigah,Andrew Parsons,Kurt Douglas,Nils Deppe,Edward Weber,GEORGINA MARTINEZ-CANIZALES,ANA CRISTINA CHIRINOS MARTINEZ,rebecca murphy,Naíde Müller C.,Vinícius Dantas,Richard Southern,Adela Abelleira,Mark Mitchell,Melanie Oliveira Neiva Santos,REINA CLEOPATRA MESTANZA PAEZ,SERENA RUGGERI,Yanbei Zhang,Melissa Atkinson,ZHIJIE CHUA,Marília Cid,Rudolph Fredua-Agyeman,Roelie Hempel,Maxim Zinchenko,Zhaoguang Xu,Alexander Holste,María Gabriela Di Barbaro,Gilmar Antônio Nava,John Fitzgerald,J Catja Warmelink,Christina Stuelten,Carlos Ángel Ordás,Felipe Tafoya,Joana Corrêa Monteiro,Carolyn Plateau,Maciej Strzemski,GIULIO CAZZOLI,Tommaso Macrì,Deniz Tasdemir,Houshang Najafi,Maria Gregou,Kevin Dadaczynski,Robert Lohmayer,Robin Rodd,Immacolata Aulisa,Sarah Patterson,昆 黄,Ke Teng,Mark Green,Elizabete Albernaz,Laura Carnevale,Fengjie li,Libor Barto,Adriano Casulli,Angelo CHIELLI,María del Carmen Arau Ribeiro,Shihan Yang,Pradeep Dewapriya,Margarida Martins Barroso,Motoaki Morita,Louis Stancato,Saher Albatran,Moeses Andrigo Danner,Yee Kin Tsui,Daniel Francés,Zoran Pesic,Nina Marie Sigvardsen,Timon Idema,Silvia J. Pech-Campos,Anurag Sunpapao,Beatriz Melero,Martina Blümel,Biyun Fang,Mihaela Ghenta,William Peirson,Hiroshi Hakoyama,Dominique Faria,Marina Recalde,María Teresa de Andres ,Ricardo Pereira,Satyanarayana Sirasani,Atta Kwami,Facundo Asia,Paula Ramos Nogueira,Alfonso Serano-Mailo,Ralph Freese,FLAVIO ANTIQUEIRA,María Teresa Ronco,Gyselle Baccan,Tuomas Tammisto,R Arroyo-Garcia,Sigifredo de Jesús Herrón Osorio,daniele santoro,Nicole Santos Accioly,Fernanda Maria Gomes da Costa Teixeira Marques,James Liebig,Patricia Gómez,Safak Kalindamar,Michele Droz dit Busset,Albertina Oliveira,Patrícia João,Umesh Sahoo,Peter Wolsing,MARTHA LUCIA MARQUEZ RESTREPO,Nils Ukley,Christian Richardt,Nuno Pedroso,Vera Mazurak,Dan Garcia-Carrillo,Kelsie Forbush,Grete Helen Meisfjord Jørgensen,Sammy Njenga,Maria Angeles Fernandez-Zamudio,BENJAMIN JUAN GOMEZ MOLINER,María Isabel Menéndez Menéndez,Agnieszka Dwojak-Matras,Serena Wright,Sandra Varnaitė-Žuravliova,Tanya Eadie,Philip Boughton,viktor vus,María José Sampedro Vizcaya,Jens Jakob Ellebæk,Milan Stojanovic,Margarida Coelho,Marta Ferrer-García,Marcelo Dos Santos Mamed,LYDIA KAMARUZAMAN,Eliana Fernandes,Jannie Fries Linnebjerg,Hossam Faheem,Janet Lydecker,Mark Clemente Arenas,Ana Melo,Rita Araújo,Ana Paula Monte,Gerard Lazo,Antonio Aguilera,Stuart Caldwell,Ahmad Al-Dweik,Marc Elie,Dolores Ponte,Santosh Varughese,Brian O'Meara,Frida Sandberg,Jorge Hernán Salazar Trujillo,Shirin Pourafshar,Pär Hallberg,Ravindra Shinde,Johan Strang,Celal Şalçini,Eduardo Díaz Amado,György Nagy,Pedro Oliver Olmo,Plinho Hertz,Alberto Rodríguez Barcón,Kara Perks,Ana Paula Prata,lurdes babo,Ziru Li,G. Muhiuddin,Nicola Personeni,Marcos-A. López-Suárez,Roger Jovani,Matthias Bartelt,Fernando Marques,John Campbell,Antonios Dakanalis,Pau Casanellas,Andrew Barnes,Helena Malmström,Janusz Blaszkowski,Hongding Gao,Dieter Rickenmann,Neville Curtis,BinVa/Bin-Wha/Ping-Hua Chang,Risto Aarne Olavi Kasanen,Isabel Araújo,António Borges Fernandes,Hilda Aguilar Grieder,Helene Niculita-Hirzel,André Fernandes,Courtenay Norbury,Ana Raquel Simões,Porfirio Sanz Camañes,Klaus Stiller,Tandi Matsha,Jens Beckert,Niels Dohn,Sergey Kravtsov,Frans-Willem Korsten,Manus Biggs,Pierre Couppie,Elisabeth Brito,Jan Tønnesvang,LORENZO SCILLITANI,José Miguel Olano,Trevor Steward,Silvia Tolu,Luis Enrique Otero Carvajal,piera maccagnani,Piotr Nowak,philippe solano,Sofia Gaspar,Patrícia Sá,Anita Quiles,Mahdi Naghshvarianjahromi,ALFEU ZANOTTO-FILHO,Ming-Cheng Luo,Joseph T Eastman,Sean Hesselbacher,Rytas Vilgalys,Ghada Bassioni,Dana Hancock,Margarida M. Pinheiro,Maksymilian Drozdowicz,Ana Cristina Pessoa Tavares dos Santos,Piotr Gleń,Jonathan Puddick,Shreyansh Shah,Richard Hartley,Dieter Schramm,Nikolai PAVLICHENKO,Zdenek Drahota,Olga Berdugina,Vitor Rodrigues,Hong-Oanh Nguyen,Carito Guziolowski,Cristina Rocha,Fernando Martinez de Toda,Prabaharan M,ana rodrigues,Clarine van Oel,Simone Alin,Bob Giddings,Ana Sofia Rodrigues,Raquel Chaves,Henk Huijser,Stephan Schmid,Pietro Gori,Ivana Noble,Ana Paula Macedo,Daria Matczyńska,Thies Pfeiffer,Xin Wang,Erica Bisesi,Manuel Silva,Tal Oron-Gilad,Poul Erik Grohnheit,Aurea de Carvalho Costa,Hans Deckmyn,Matilda Hellman,Teresa Ferreira,Alsones Balestrin,Hannes Zechlin,Will Allen,Benoît Valley,Arthur Kilcoyne,Matt Visser,Henrique ,Oriana Mansutti,长彦 田,Hector Monterde-i-Bort,Stefania Castelletto,Felisbela Lopes,Elaine Jeffreys,Patrik Schumacher,Teik-Thye Lim,Tanja M. Kneiske,Yeau-Ren Jeng,Geoff Kent,Carsten Dahl Mørch,Ezequiel Di Paolo,Adamantia Paizis,Leonor Pais
+986 authors
,Richard WhiteJournal
Published
Jul 29, 2010
Show more
Save
Tip0
TipSave
arXiv:1007.5145v1 [hep-th] 29 Jul 2010
CPHT-RR054.0710
DESY 10-115
OUTP-10/16P
One-loop Yukawa Couplings in Local Models
Joseph P. Conlon 1,2 , Mark Goodsell 3 and Eran Palti 4
1 Rudolf Peierls Center for Theoretical Physics, 1 Keble Road,
Oxford, OX1 3NP, United Kingdom
2 Balliol College, Oxford, OX1 3BJ, United Kingdom
3 Deutsches Elektronen-Synchrotron DESY, Notkestrasse 85, D-22603 Hamburg, Germany.
4 Centre de Physique Theorique, Ecole Polytechnique, CNRS, 91128 Palaiseau, France.
j.conlon1@physics.ox.ac.uk, mark.goodsell@desy.de, eran.palti@cpht.polytechnique.fr
Abstract
We calculate the one-loop Yukawa couplings and threshold corrections for supersymmetric local models
of branes at singularities in type IIB string theory. We compute the corrections coming both from
wavefunction and vertex renormalisation. The former comes in the IR from conventional field theory
running and in the UV from threshold corrections that cause it to run from the winding scale associated
to the full Calabi-Yau volume. The vertex correction is naively absent as it appears to correspond
to superpotential renormalisation. However, we find that while the Wilsonian superpotential is not
renormalised there is a physical vertex correction in the 1PI action associated to light particle loops.
CPHT-RR054.0710
DESY 10-115
OUTP-10/16P
One-loop Yukawa Couplings in Local Models
Joseph P. Conlon 1,2 , Mark Goodsell 3 and Eran Palti 4
1 Rudolf Peierls Center for Theoretical Physics, 1 Keble Road,
Oxford, OX1 3NP, United Kingdom
2 Balliol College, Oxford, OX1 3BJ, United Kingdom
3 Deutsches Elektronen-Synchrotron DESY, Notkestrasse 85, D-22603 Hamburg, Germany.
4 Centre de Physique Theorique, Ecole Polytechnique, CNRS, 91128 Palaiseau, France.
j.conlon1@physics.ox.ac.uk, mark.goodsell@desy.de, eran.palti@cpht.polytechnique.fr
Abstract
We calculate the one-loop Yukawa couplings and threshold corrections for supersymmetric local models
of branes at singularities in type IIB string theory. We compute the corrections coming both from
wavefunction and vertex renormalisation. The former comes in the IR from conventional field theory
running and in the UV from threshold corrections that cause it to run from the winding scale associated
to the full Calabi-Yau volume. The vertex correction is naively absent as it appears to correspond
to superpotential renormalisation. However, we find that while the Wilsonian superpotential is not
renormalised there is a physical vertex correction in the 1PI action associated to light particle loops.
Contents
1 Introduction 2
2 CFT Building Blocks 3
2.1 Vertex operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2 Bosonic Correlators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2.1 Internal untwisted quantum correlators . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2.2 Momentum exponential correlators and pole structures . . . . . . . . . . . . . . . . 7
2.3 Fermionic and Ghost Correlators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.4 Partition functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.5 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3 Yukawa threshold corrections 11
3.1 General structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.2 3-point amplitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.3 4-point amplitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4 Summary and discussion 28
A Gauge Threshold Corrections 29
B Theta Identities 32
C Determination of Amplitude via Lorentz Structure 33
1 Introduction
Loop corrections to effective actions play an important general role in physics. Supersymmetric theories
are celebrated for their special behaviour at loop level and for the protection of holomorphic properties
against renormalisation. Specifically, the superpotential does not get perturbatively renormalised and the
gauge kinetic function is perturbatively renormalised only at one-loop. The study of one-loop gauge cou-
plings and their threshold corrections has been carried out extensively in both field and string theory. In
this context there is an important distinction between the Wilsonian gauge kinetic function, renormalised
only at one-loop, and the physical coupling, which is corrected at all orders. The study of one-loop
Yukawa couplings in string theory has been less extensive, and the distinction between holomorphic and
physical couplings less clearly drawn. Here holomorphy properties have been taken to imply that Yukawa
couplings only receive one-loop corrections from wavefunction renormalisation.
2
1 Introduction 2
2 CFT Building Blocks 3
2.1 Vertex operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2 Bosonic Correlators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2.1 Internal untwisted quantum correlators . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2.2 Momentum exponential correlators and pole structures . . . . . . . . . . . . . . . . 7
2.3 Fermionic and Ghost Correlators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.4 Partition functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.5 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3 Yukawa threshold corrections 11
3.1 General structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.2 3-point amplitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.3 4-point amplitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4 Summary and discussion 28
A Gauge Threshold Corrections 29
B Theta Identities 32
C Determination of Amplitude via Lorentz Structure 33
1 Introduction
Loop corrections to effective actions play an important general role in physics. Supersymmetric theories
are celebrated for their special behaviour at loop level and for the protection of holomorphic properties
against renormalisation. Specifically, the superpotential does not get perturbatively renormalised and the
gauge kinetic function is perturbatively renormalised only at one-loop. The study of one-loop gauge cou-
plings and their threshold corrections has been carried out extensively in both field and string theory. In
this context there is an important distinction between the Wilsonian gauge kinetic function, renormalised
only at one-loop, and the physical coupling, which is corrected at all orders. The study of one-loop
Yukawa couplings in string theory has been less extensive, and the distinction between holomorphic and
physical couplings less clearly drawn. Here holomorphy properties have been taken to imply that Yukawa
couplings only receive one-loop corrections from wavefunction renormalisation.
2
In this paper we study one-loop Yukawa couplings for supersymmetric models of branes at singularities
in type IIB string theory. These models are local in the sense that for much of the calculation the global
compact completion of the internal manifold does not play a role [1]. Previous studies of one-loop Yukawa
couplings in heterotic and type IIA settings have been performed in [2–5]. There are two important
motivations for this work. The first is that the one-loop behaviour of running couplings in local models
is especially interesting with respect to the volume of the full global manifold. For gauge threshold
corrections, studied in [6–8], gauge couplings run to a scale set by the global volume of the manifold,
the so called winding scale, rather than the local string scale. This has important consequences both
practically, as for the case of local GUT models it implies the string scale is an order of magnitude below
the GUT scale, and conceptually, in the sense of understanding the extent to which a local model can
be decoupled from the bulk. It is natural to investigate the same behaviour for Yukawa couplings, where
indeed we find precisely this property, with UV threshold corrections implying that the Yukawas are
renormalised up to the winding scale rather than the naive cutoff, the local string scale.
The second motivation arose during the calculation and involves the distinction between physical
and holomorphic couplings. In [9–11] it was argued that for supersymmetric field theories with massless
particles, in apparent contradiction to the non-renormalisation theorem, it is possible for superpotential
operators to receive finite loop corrections that are not associated to wavefunction renormalisation. In the
case of Yukawa couplings this corresponds to vertex renormalisation. The vertex correction is generated
in the IR by integrating over light loop momenta. While the Wilsonian superpotential - corresponding
to an action at a scale E with light modes yet to be integrated over - is not renormalised, the vertex
correction is a physical feature of the 1PI action. We find that local models of branes at singularities
(and we expect also more general intersecting brane constructions) fall within this class of theories. We
demonstrate explicit one-loop vertex renormalisation from the world-sheet perspective thereby giving, to
our knowledge, the first realisation of this effect in string theory.
The paper is structured as follows. In section 2 we review the basic CFT building blocks that are
needed for the computation. This section establishes notation and convention, as well as reviewing bosonic
and fermionic correlators on the torus and annulus. We also introduce the model that we study throughout
this paper: fractional D3 branes on the C3/Z4 orbifold. Section 3 contains the main calculation. We first
compute the one-loop Yukawas via a 3-point scattering amplitude computation. This demonstrates the
key renormalisation properties of the Yukawas but also contains some ambiguities regarding the off-shell
continuation. We subsequently resolve these by performing a 4-point calculation that reduces to the 3-
point amplitude in a certain limit. We describe the structure of the string diagram and how it generates
both wavefunction and vertex renormalisation. In section 4 we present a summary and discussion of our
results. The appendix contains a warm-up calculation of gauge threshold corrections as well as various
properties of ϑ-functions.
2 CFT Building Blocks
The computation of the amplitudes requires the evaluation of various CFT correlators between world-sheet
fields that are introduced through the vertex operators. In this section we collate the relevant correlators
and also other miscellaneous CFT results that are used. An incomplete list of useful references for
these CFT correlators are [4, 18–26]. All the amplitudes evaluated in this paper are cylinder (annulus)
3
in type IIB string theory. These models are local in the sense that for much of the calculation the global
compact completion of the internal manifold does not play a role [1]. Previous studies of one-loop Yukawa
couplings in heterotic and type IIA settings have been performed in [2–5]. There are two important
motivations for this work. The first is that the one-loop behaviour of running couplings in local models
is especially interesting with respect to the volume of the full global manifold. For gauge threshold
corrections, studied in [6–8], gauge couplings run to a scale set by the global volume of the manifold,
the so called winding scale, rather than the local string scale. This has important consequences both
practically, as for the case of local GUT models it implies the string scale is an order of magnitude below
the GUT scale, and conceptually, in the sense of understanding the extent to which a local model can
be decoupled from the bulk. It is natural to investigate the same behaviour for Yukawa couplings, where
indeed we find precisely this property, with UV threshold corrections implying that the Yukawas are
renormalised up to the winding scale rather than the naive cutoff, the local string scale.
The second motivation arose during the calculation and involves the distinction between physical
and holomorphic couplings. In [9–11] it was argued that for supersymmetric field theories with massless
particles, in apparent contradiction to the non-renormalisation theorem, it is possible for superpotential
operators to receive finite loop corrections that are not associated to wavefunction renormalisation. In the
case of Yukawa couplings this corresponds to vertex renormalisation. The vertex correction is generated
in the IR by integrating over light loop momenta. While the Wilsonian superpotential - corresponding
to an action at a scale E with light modes yet to be integrated over - is not renormalised, the vertex
correction is a physical feature of the 1PI action. We find that local models of branes at singularities
(and we expect also more general intersecting brane constructions) fall within this class of theories. We
demonstrate explicit one-loop vertex renormalisation from the world-sheet perspective thereby giving, to
our knowledge, the first realisation of this effect in string theory.
The paper is structured as follows. In section 2 we review the basic CFT building blocks that are
needed for the computation. This section establishes notation and convention, as well as reviewing bosonic
and fermionic correlators on the torus and annulus. We also introduce the model that we study throughout
this paper: fractional D3 branes on the C3/Z4 orbifold. Section 3 contains the main calculation. We first
compute the one-loop Yukawas via a 3-point scattering amplitude computation. This demonstrates the
key renormalisation properties of the Yukawas but also contains some ambiguities regarding the off-shell
continuation. We subsequently resolve these by performing a 4-point calculation that reduces to the 3-
point amplitude in a certain limit. We describe the structure of the string diagram and how it generates
both wavefunction and vertex renormalisation. In section 4 we present a summary and discussion of our
results. The appendix contains a warm-up calculation of gauge threshold corrections as well as various
properties of ϑ-functions.
2 CFT Building Blocks
The computation of the amplitudes requires the evaluation of various CFT correlators between world-sheet
fields that are introduced through the vertex operators. In this section we collate the relevant correlators
and also other miscellaneous CFT results that are used. An incomplete list of useful references for
these CFT correlators are [4, 18–26]. All the amplitudes evaluated in this paper are cylinder (annulus)
3
100%
