{"created":"2023-06-20T13:23:17.183688+00:00","id":4067,"links":{},"metadata":{"_buckets":{"deposit":"86c68f3f-5676-48d9-899e-b6b39916a337"},"_deposit":{"created_by":21,"id":"4067","owners":[21],"pid":{"revision_id":0,"type":"depid","value":"4067"},"status":"published"},"_oai":{"id":"oai:ir.soken.ac.jp:00004067","sets":["2:428:16"]},"author_link":["2250","2251","2252"],"item_1_creator_2":{"attribute_name":"著者名","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"本多, 正純"}],"nameIdentifiers":[{}]}]},"item_1_creator_3":{"attribute_name":"フリガナ","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"ホンダ, マサズミ"}],"nameIdentifiers":[{}]}]},"item_1_date_granted_11":{"attribute_name":"学位授与年月日","attribute_value_mlt":[{"subitem_dategranted":"2013-03-22"}]},"item_1_degree_grantor_5":{"attribute_name":"学位授与機関","attribute_value_mlt":[{"subitem_degreegrantor":[{"subitem_degreegrantor_name":"総合研究大学院大学"}]}]},"item_1_degree_name_6":{"attribute_name":"学位名","attribute_value_mlt":[{"subitem_degreename":"博士（理学）"}]},"item_1_description_12":{"attribute_name":"要旨","attribute_value_mlt":[{"subitem_description":"Numerical test of AdS/CFT correspondence for M2-branes\nM-theory is an eleven-dimensional theory, which has been proposed as a strong coupling limit\nof the type IIA superstring theory. It has been also expected that the M-theory includes the\neleven-dimensional supergravity (11d SUGRA) as a low-energy limit. The 11d SUGRA consists\nof the graviton, gravitino and three-form gauge field. The three-form field in eleven dimensions\nelectrically (magnetically) couples to two(five)-dimensional object. Such objects naturally appear\nas black brane solutions conserving a part of supersymmetries in the 11d SUGRA. On the\nanalogy of the relation between such solutions in the ten-dimensional supergravities and objects\nin the superstring theories as string, NS5-brane and D-branes, we can expect that the M-theory\nhas fundamental two- and five-dimensional objects. These objects are called as ``M2-brane``\nand ``M5-brane``, respectively. In this thesis, we focus on Physics of the multiple M2-branes.\nAs well known, a low-energy limit of parallel N Dp-branes is described by the (p+1)-dimensional\nU(N) maximally supersymmetric Yang-Mills theory. This U(N) gauge symmetry can be\nintuitively understood by the facts that open string includes spin-1 massless boson in its spectrum\nand have an U(1) charge called as a Chan-Paton factor. What is a low-energy effective\ntheory of the parallel N M2-branes? Unfortunately, we have not an established answer to this\nquestion yet as we will argue below.\nFrom the single M2-brane analysis and implication of the AdS/CFT correspondence, we\nexpect that the low energy effective theory for $N$ M2-branes has the following properties:\n(1) Three dimensional conformal symmetry, (2) N=8 supersymmetry, (3) SO(8) R-symmetry,\nand so on.\nHowever, such a theory had not been found for long years. There are many reasons for this.\nOne of most serious obstacle is difficulty of quantization of supermembrane. This prevents us\nfrom finding spectrum and something like a Chan-Paton factor for M2-branes. Another difficult\n-ty is that it is not easy to construct gauge theory with conformal and high supersymmetry\nexcept for four dimensions. Since Yang-Mills action is scale invariant only for four dimensionns,\nwe can use only Chern-Simons term of vector multiplet and marginal term of chiral multiplet\nfor the construction. Indeed in 1990's, a maximal supersymmetric extension of Chern-\nSimons theory had been N=3.\nIn 2008, Aharony, Bergman, Jafferis and Maldacena (ABJM) has proposed a U(N)xU(N)\ntheory with Chern-Simons levels k and -k coupled to bi-fundamental matters. This theory has\nN=8 supersymmetry for k=1,2 and N=6 supersymmetry for other values of k. It has been\nconjectured tobe dual to M-theory on AdS_4 x S^7/Z_k for k<<N^{1/5}, and to type IIA\nsuperstring onAdS_4xCP^3 in the planar large-N limit with the 't Hooft coupling constant λ=N/\nk kept fixed. From the viewpoint of quantum gravity, the ABJM theory is important since it\nmay provide us with a nonperturbative definition of type IIA superstring theory or M-theory\non AdS_4 back-grounds since the theory is well-defined for finite N. One may draw a precise\nanalogy with the way maximally supersymmetric Yang-Mills theories may provide us with non\nperturbative formulations of type IIA/IIB superstring theories on D-brane backgrounds through\nthe gauge/gravity duality. In particular, the M-theory limit is important given that M-theory is\nnot defined even perturbatively, although there is a well-known conjecture on its nonperturbative\nformulation in the infinite momentum frame in terms of matrix quantum mechanics. The\nplanar limit, which corresponds to type IIA superstring theory, has interest on its own since it\nmay allow us to perform more detailed tests of the gauge/gravity duality than in the case of\nAdS_5/CFT_4. In particular, we may hope to calculate the 1/N corrections to the planar limit,\nwhich enables us to test the gauge/gravity duality at the quantum string level, little of which\nis known so far.\nIn all these prospectives, one needs to study the ABJM theory in the strong coupling regime.\nAs in the case of QCD, it would be nice if one could study the ABJM theory on a lattice by\nMonte Carlo methods. This seems quite difficult, though, for the following three reasons.\nFirstly, the construction of the Chern-Simons term on the lattice is not straightforward,\nalthough there is a proposal based on its connection to the parity anomaly. Secondly, the\nChern-Simons term is purely imaginary in the Euclidean formulation, which causes a technical\nproblem known as the sign problem when one tries to apply the idea of importance sampling.\nThirdly, the lattice discretization necessarily breaks supersymmetry, and one needs to restore it\nin the continuum limit by fine-tuning the coupling constants of the supersymmetry breaking\nrelevant operators. This might, however, be overcome by the use of a non-lattice regularization\nof the ABJM theory based on the large-N reduction on S^3, which is shown to be useful in\nstudying the planar limit of the 4d N=4 super Yang-Mills theory.\nIn this thesis, we show that the ABJM theory can be studied for arbitrary N at arbitrary cou\npling constant by applying a simple Monte Carlo method to the matrix model that can be deri\nved from the theory by using the localization technique. This opens up the possibility of\nprobing the quantum aspects of M-theory and testing the AdS_4/CFT_3 duality at the quantum\nlevel. Here we calculate the free energy, and confirm the N^3/2 scaling in the M-theory limit\npredicted from the gravity side. We also find that our results nicely interpolate the analytical\nformulae proposed previously in the M-theory and type IIA regimes. Furthermore, we show\nthat some results obtained by the Fermi gas approach can be clearly understood from the\nconstant map contribution obtained by the genus expansion. The method can be easily\ngeneralized to the calculations of BPS operators and to other theories that reduce to matrix\nmodels. We also study the super-symmetric Wilson loops in the ABJM theory. Our result\nnicely interpolates the expressions at weak and strong coupling regions.","subitem_description_type":"Other"}]},"item_1_description_7":{"attribute_name":"学位記番号","attribute_value_mlt":[{"subitem_description":"総研大甲第1590号 ","subitem_description_type":"Other"}]},"item_1_select_14":{"attribute_name":"所蔵","attribute_value_mlt":[{"subitem_select_item":"有"}]},"item_1_select_8":{"attribute_name":"研究科","attribute_value_mlt":[{"subitem_select_item":"高エネルギー加速器科学研究科"}]},"item_1_select_9":{"attribute_name":"専攻","attribute_value_mlt":[{"subitem_select_item":"14 素粒子原子核専攻"}]},"item_1_text_10":{"attribute_name":"学位授与年度","attribute_value_mlt":[{"subitem_text_value":"2012"}]},"item_creator":{"attribute_name":"著者","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"HONDA, Masazumi ","creatorNameLang":"en"}],"nameIdentifiers":[{}]}]},"item_files":{"attribute_name":"ファイル情報","attribute_type":"file","attribute_value_mlt":[{"accessrole":"open_date","date":[{"dateType":"Available","dateValue":"2016-02-26"}],"displaytype":"simple","filename":"甲1590_要旨.pdf","filesize":[{"value":"287.7 kB"}],"format":"application/pdf","licensetype":"license_11","mimetype":"application/pdf","url":{"label":"要旨・審査要旨","url":"https://ir.soken.ac.jp/record/4067/files/甲1590_要旨.pdf"},"version_id":"cbd22254-bf97-41a3-b2d9-69a8b578e32f"},{"accessrole":"open_date","date":[{"dateType":"Available","dateValue":"2016-02-17"}],"displaytype":"simple","filename":"甲1590_本文.pdf","filesize":[{"value":"1.7 MB"}],"format":"application/pdf","licensetype":"license_11","mimetype":"application/pdf","url":{"label":"本文","url":"https://ir.soken.ac.jp/record/4067/files/甲1590_本文.pdf"},"version_id":"f7384dae-fb93-41da-94c0-aff54829ce9b"}]},"item_language":{"attribute_name":"言語","attribute_value_mlt":[{"subitem_language":"eng"}]},"item_resource_type":{"attribute_name":"資源タイプ","attribute_value_mlt":[{"resourcetype":"thesis","resourceuri":"http://purl.org/coar/resource_type/c_46ec"}]},"item_title":"Numerical test of AdS/CFT correspondence for M2-branes","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"Numerical test of AdS/CFT correspondence for M2-branes"},{"subitem_title":"Numerical test of AdS/CFT correspondence for M2-branes","subitem_title_language":"en"}]},"item_type_id":"1","owner":"21","path":["16"],"pubdate":{"attribute_name":"公開日","attribute_value":"2013-11-15"},"publish_date":"2013-11-15","publish_status":"0","recid":"4067","relation_version_is_last":true,"title":["Numerical test of AdS/CFT correspondence for M2-branes"],"weko_creator_id":"21","weko_shared_id":21},"updated":"2023-06-20T15:15:05.421550+00:00"}