[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-42813-en":3,"doc-seo-42813-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},42813,1099513958607,"Jiven","https://ap-avatar.wpscdn.com/avatar/100002390cf8733938c?x-image-process=image/resize,m_fixed,w_180,h_180&k=1778829742770036399",8,"Research & Report","The Statistics of Supersymmetric D-brane Models","We investigate the statistics of the phenomenologically important D-brane sector of string compactifications. For intersecting D-brane models, number-theory-inspired methods determine the asymptotic distribution of solutions to tadpole cancellation conditions. The work computes statistical distributions of gauge-theory observables, including gauge-group rank, the number of chiral generations, and the probability of an SU(N) gauge factor. Studies focus on intersecting branes on T2 and T4/ZZ2 and T6/ZZ2×ZZ2 orientifolds, revealing correlations between gauge rank and chiral generation count and effects of coupling the gauge and flux sectors.","arXiv :hep-th/ 04 1 1 17 3v 3 16 Dec 2004  \nMPP-2004-147 LMU-TPS 04/13 hep-th/0411173  \nThe Statistics of Supersymmetric D-brane Models  \nRalph Blumenhagena , Florian Gmeinera , Gabriele Honeckera , Dieter L¨usta,b and Timo Weiganda  \na Max-Planck Institut f¨ur Physik, F¨ohringer Ring 6, 80805 M¨unchen, Germany  \ne-mail: blumenha, flo, gabriele, luest, [weigand@mppmu.mpg.de](weigand@mppmu.mpg.de)  \nbDepartment f¨ur Physik, Ludwig-Maximilians-Universit¨at M¨unchen Theresienstra􀀙e 37, 80333 M¨unchen, Germany e-mail: [luest@theorie.physik.uni-muenchen.de](luest@theorie.physik.uni-muenchen.de)  \nAbstract  \nWe investigate the statistics of the phenomenologically important D-brane sector of string compacti􀀌cations. In particular for the class of intersecting D-brane models, we generalise methods known from number theory to determine the asymptotic statistical distribution of solutions to the tadpole cancellation conditions. Our approach allows us to compute the statistical distribution of gauge theoretic observables like the rank of the gauge group, the number of chiral generations or the probability of an SU(N) gauge factor. Concretely, we study the statistics of intersecting branes on T 2 and T4 /ZZ2 and T6 /ZZ2 × ZZ2 orientifolds. Intriguingly, we 􀀌nd a statistical correlation between the rank of the gauge group and the number of chiral generations. Finally, we combine the statistics of the gauge theory sector with the statistics of the 􀀍ux sector and study how distributions of gauge theoretic quantities are a􀀋ected.  \n1. Introduction  \nFor many years, string theorists have studied various kinds of string compacti􀀌cations with the main motivation to 􀀌nd a model one day which resembles the Standard Model of particle physics, which we know is a good e􀀋ective description of nature around the weak scale. Of course, it is very compelling that string theory in some sense predicts (or at least contains) gravity and at the same time also gauge theory, but it turned out to be a very di􀀎cult problem to be more precise about the predictions for the gauge theory sector at low energies. There were simply too many possible candidates which at best resembled the Standard Model in certain aspects but not in its full glory. However, one could also say that if we had constructed the Standard Model already in a few attempts, we could have simply been very lucky or more probably would have just found one of a vast number of stringy realizations of the Standard Model.  \nRecall that in the eighties the weakly coupled heterotic string was thought to bethe best candidate to deliver a realistic model. Various (supersymmetric) constructions, like orbifolds, bosonic lattices, free fermion constructions, Calabi-Yau manifolds in toric varieties, Landau-Ginzburg and Gepner models etc. were studied and partly classi􀀌ed ina large number of publications. Even today it is not clear whether there exist 􀀌nitely orin􀀌nitely many heterotic string backgrounds.  \nWith the advent of D-branes in the mid nineties, new classes of phenomenologically attractive string compacti􀀌cations were found where the gauge theory is realized by the open strings ending on D-branes. Di􀀋erent constructions were proposed like orientifolds with branes on singularities or intersecting D-branes. It was also realized that the string scale does not necessarily have to be close to the Planck scale, as in D-brane constructionslow string scale models can exist and would lead to a completely new phenomenology in the TeV range [1] . In this case, supersymmetry would no longer be necessary for solving the gauge hierarchy problem.  \nIn addition, with the extension of the relevant dimensions to eleven and even twelve, new geometric compacti􀀌cations were possible like M-theory on G2 manifolds or F-theory on Calabi-Yau fourfolds. Since among these di􀀋erent classes of string models various S and T dualities operate, not all constructions were considered to be independent, but rather provide descriptions in","cbCaitPADP2H7zbD","https://ap.wps.com/l/cbCaitPADP2H7zbD","pdf",716470,2,1,62,"English","en",105,"# Abstract\n# Introduction","[{\"question\":\"What is the main goal of the study?\",\"answer\":\"To determine the asymptotic statistical distribution of solutions to tadpole cancellation conditions in intersecting D-brane models and to connect these distributions to gauge-theory observables.\"},{\"question\":\"Which gauge-theory observables are analyzed statistically?\",\"answer\":\"The study computes distributions for the gauge-group rank, the number of chiral generations, and probabilities for gauge factors such as SU(N).\"},{\"question\":\"What correlation is found in the statistical results?\",\"answer\":\"A statistical correlation is reported between the rank of the gauge group and the number of chiral generations.\"}]",1783371721,156,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"the-statistics-of-supersymmetric-d-brane-models","",{"@graph":36,"@context":85},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,47,50],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":20},"https://docshare.wps.com/document/","Document",{"item":48,"name":12,"@type":43,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":43,"position":52},"https://docshare.wps.com/document/the-statistics-of-supersymmetric-d-brane-models/42813/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":24,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-11","2026-07-06",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What is the main goal of the study?","Question",{"text":75,"@type":76},"To determine the asymptotic statistical distribution of solutions to tadpole cancellation conditions in intersecting D-brane models and to connect these distributions to gauge-theory observables.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"Which gauge-theory observables are analyzed statistically?",{"text":80,"@type":76},"The study computes distributions for the gauge-group rank, the number of chiral generations, and probabilities for gauge factors such as SU(N).",{"name":82,"@type":73,"acceptedAnswer":83},"What correlation is found in the statistical results?",{"text":84,"@type":76},"A statistical correlation is reported between the rank of the gauge group and the number of chiral generations.","https://schema.org",{"og:url":51,"og:type":87,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":89,"canonical":51},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,135],{"id":21,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":20,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":52,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":46,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":46,"category_name":137,"show_sort_weight":106,"slug":138},19,"General","general"]