[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-150242-en":3,"doc-seo-150242-105":29,"detail-sidebar-cat-0-en-105":90},{"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":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":11,"language":21,"language_code":22,"site_id":23,"html_lang":22,"table_of_contents":24,"faqs":25,"seo_title":26,"seo_description":14,"update_tm":27,"read_time":28},150242,3985741905716,"Kyle","https://ap-avatar.wpscdn.com/davatar_994ba38a5ba835b3df7d355c54d3ed8d",8,"Research & Report","Unification of Gravities with GUTs","本文基于引力的规范理论框架，研究在四维时空的切线空间扩展对称性进行规范化，从而将引力与内部相互作用统一。文章以SO(10)为GUT基础，讨论共形引力与非对易(模糊)引力在内部相互作用中的统一实现。内容涵盖该方法的理论动机，以及在构造四维手征规范理论时需满足的Weyl与Majorana等约束条件，并概述共形引力凝聚到爱因斯坦引力或Weyl尺度不变引力的自发对称破缺机制。","Unification of Gravities with GUTs  \nD. Roumelioti a,1, S. Stefas a,2, G. Zoupanos a,b,c,d,3  \na Physics Department, National Technical University of Athens, Zografou Campus, 157 80,  \nZografou, Greece  \nb Max-Planck Institut f¨ur Physik, Boltzmannstr. 8, 85 748 Garching/Munich, Germany  \nc Universit¨at Hamburg, Luruper Chaussee 149, 22 761 Hamburg, Germany d Deutsches Elektronen-Synchrotron DESY, Notkestraße 85, 22 607, Hamburg, Germany  \nWithin the gauge-theoretic approach of gravity, the gauging of an enlarged symmetry of the tangent space in four dimensions allows gravity to be unified with internal interactions. We study the unification of the Conformal and Noncommutative (Fuzzy) Gravities with Internal Interactions based on the SO(10) GUT.  \n1. Introduction  \nIn addition to the well-known fact that the Standard Model of Particle Physics is described very successfully by gauge theories, it has long been believed that general relativity (GR) can be formulated as a gauge theory [1–7] too. Furthermore, a very interesting suggestion towards unifying gravity as gauge theory with the rest fundamental interactions described as GUTs, has been suggested a few decades ago [8 , 9] and revived recently [10–18] . It is based on the observation that although the dimension of the tangent space is usually taken to be equal to the dimension of the corresponding curved manifold, the tangent group of a manifold of dimension d is not necessarily SO (d) [19] . This observation provides us with the very interesting possibility to consider tangent groups of dimension higher than four, in a 4-d spacetime, which in turn could lead to a unification of gravity with internal interactions by gauging these higher-dimensional tangent groups. A very attractive feature of this approach is that most of the tools which have been used in the high dimensional theories with extra physical space dimensions, such as in the cosetspace dimensional reduction (CSDR) scheme [20–29], can be transferred in the present four-dimensional framework since they have the same tangent group. For instance, there exist constraints which one has to take into account aiming to construct realistic chiral gauge theories describing the internal interactions. An example of such constraint is the Weyl condition that one has to impose in the extra-dimensional gauge theory in order to obtain a chiral one in 4-d. Similarly to avoid a possible doubling of the spectrum in a constructed 4-d chiral gauge theory one has to impose in addition to the Weyl also the Majorana condition in the higher-dimensional one [22 , 25] .  \nAlong the lines described above, a unification of Conformal Gravity (CG) and internal interactions has been constructed recently [18] . This approach was subsequently extended to the unification of 4-d Gravity on a covariant noncommutative (fuzzy) space, i.e. Fuzzy gravity (FG) with internal interactions [30] . Here, we present the basic features of these constructions.  \n1 E-mail: [danai_roumelioti@mail.ntua.gr](danai_roumelioti@mail.ntua.gr)  \n2 E-mail: [dstefas@mail.ntua.gr](dstefas@mail.ntua.gr)  \n3 E-mail: [george.zoupanos@cern.ch](george.zoupanos@cern.ch)  \n2  \n2. Conformal Gravity  \nThe Einstein Gravity (EG) has been treated as the gauge theory of the Poincar´e group [2] but much insight and elegance was gained by considering instead the gauging of the de Sitter (dS) and the Anti-de Sitter (AdS) groups, SO(1 , 4) and SO(2 , 3) respectively. Both groups contain the same number of generators, i.e. 10, as the Poincar´e group and can be spontaneously broken by a scalar field to the Lorentz group, SO(1 , 3) [6 , 7 , 18 , 31] . Note, in addition, that the Poincar´e, the dS and the AdS groups are all subgroups of the conformal group SO(2 , 4), which has 15 generators. In ref [32] the gauge theory formalism of Gravity was extended to the conformal group constructing in this way the CG. The breaking of CG to EG or to Weyl’s scale invariant theory of gravity was done by the i","cbCaiflkhq21xp7m","https://ap.wps.com/l/cbCaiflkhq21xp7m","pdf",340761,1,"English","en",105,"# Introduction\n## Conformal Gravity","[{\"question\":\"本文提出了什么总体统一思路？\",\"answer\":\"在规范理论框架下，通过对四维切线空间的扩展对称性进行规范化，将引力与内部相互作用统一起来，并以SO(10) GUT为基础讨论共形与非对易(模糊)引力的统一。\"},{\"question\":\"文章中为何需要考虑更高维的切线群？\",\"answer\":\"因为切线空间的维数并不必然等于对应弯曲流形的维数，允许在四维时空中考虑维数高于四的切线群，从而借助这些更高维切线结构实现与内部相互作用的统一。\"},{\"question\":\"构造四维手征规范理论时需遵循哪些关键约束？\",\"answer\":\"文章提到需施加Weyl条件以获得四维手征规范理论；为避免谱的可能加倍，还需在更高维框架中同时施加Majorana条件。\"}]","Unification of Gravities with GUTs | PDF",1787816658,20,{"code":4,"msg":30,"data":31},"ok",{"site_id":23,"language":22,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":85,"head_meta":87,"extra_data":89,"updated_unix":27},"unification-of-gravities-with-guts","",{"@graph":35,"@context":84},[36,53,67],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":42,"position":52},"https://docshare.wps.com/document/unification-of-gravities-with-guts/150242/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":22,"description":14,"dateModified":61,"datePublished":61,"encodingFormat":60,"isAccessibleForFree":62,"interactionStatistic":63},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-08-27",true,{"@type":64,"interactionType":65,"userInteractionCount":4},"InteractionCounter",{"@type":66},"ViewAction",{"@type":68,"mainEntity":69},"FAQPage",[70,76,80],{"name":71,"@type":72,"acceptedAnswer":73},"本文提出了什么总体统一思路？","Question",{"text":74,"@type":75},"在规范理论框架下，通过对四维切线空间的扩展对称性进行规范化，将引力与内部相互作用统一起来，并以SO(10) GUT为基础讨论共形与非对易(模糊)引力的统一。","Answer",{"name":77,"@type":72,"acceptedAnswer":78},"文章中为何需要考虑更高维的切线群？",{"text":79,"@type":75},"因为切线空间的维数并不必然等于对应弯曲流形的维数，允许在四维时空中考虑维数高于四的切线群，从而借助这些更高维切线结构实现与内部相互作用的统一。",{"name":81,"@type":72,"acceptedAnswer":82},"构造四维手征规范理论时需遵循哪些关键约束？",{"text":83,"@type":75},"文章提到需施加Weyl条件以获得四维手征规范理论；为避免谱的可能加倍，还需在更高维框架中同时施加Majorana条件。","https://schema.org",{"og:url":51,"og:type":86,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":88,"canonical":51},"index,follow",{"doc_id":7,"site_id":23},{"code":4,"msg":5,"data":91},[92,96,100,104,109,114,119,122,126,129,133],{"id":20,"doc_module":4,"doc_module_name":45,"category_name":93,"show_sort_weight":94,"slug":95},"Story & Novel",90,"story-novel",{"id":46,"doc_module":4,"doc_module_name":45,"category_name":97,"show_sort_weight":98,"slug":99},"Literature",80,"literature",{"id":52,"doc_module":4,"doc_module_name":45,"category_name":101,"show_sort_weight":102,"slug":103},"Exam",70,"exam",{"id":105,"doc_module":4,"doc_module_name":45,"category_name":106,"show_sort_weight":107,"slug":108},5,"Comic",60,"comic",{"id":110,"doc_module":4,"doc_module_name":45,"category_name":111,"show_sort_weight":112,"slug":113},6,"Technology",50,"technology",{"id":115,"doc_module":4,"doc_module_name":45,"category_name":116,"show_sort_weight":117,"slug":118},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":45,"category_name":12,"show_sort_weight":120,"slug":121},30,"research-report",{"id":123,"doc_module":4,"doc_module_name":45,"category_name":124,"show_sort_weight":28,"slug":125},9,"Religion & Spirituality","religion-spirituality",{"id":28,"doc_module":4,"doc_module_name":45,"category_name":127,"show_sort_weight":28,"slug":128},"World Cup","world-cup",{"id":130,"doc_module":4,"doc_module_name":45,"category_name":131,"show_sort_weight":130,"slug":132},10,"Lifestyle","lifestyle",{"id":134,"doc_module":4,"doc_module_name":45,"category_name":135,"show_sort_weight":105,"slug":136},19,"General","general"]