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Study of Holography for Three Dimensional Spin-3 Gravity Coupled to a Scalar Field

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Please use this identifier to cite or link to this item:https://doi.org/10.14943/doctoral.k13563
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Title: Study of Holography for Three Dimensional Spin-3 Gravity Coupled to a Scalar Field
Other Titles: スカラー場と結合した3次元スピン3重力に対するホログラフィーに関する研究
Authors: 鈴木, 智貴 Browse this author
Issue Date: 25-Mar-2019
Publisher: Hokkaido University
Abstract: Since the gravitational theory is not renormalizable, it is necessary to formulate the quantum gravity by using the other framework. The AdS/CFT correspondence is one of the candidates to describe quantum gravity. According to this correspondence, a gravitational theory is equivalent to a gauge theory on the boundary, which does not contain the gravity. Although the complete proof of the AdS/CFT correspondence has not been obtained, a lot of evidence, which guarantees the existence, have been reported. In this paper, we will study the duality between the three-dimensional spin-3 gravity coupled to a scalar field and the W3 extended conformal field theory. Although the three-dimensional spin-3 gravity is well-studied owing to its equivalence with the Chern-Simons gauge theory, the spin-3 gravity coupled to matter fields is less understood. This is because the action integral of the spin-3 gravity coupled to matters is unknown. The AdS/CFT correspondence gives a new point of view. It is known that the three-dimensional spin-3 gravity is equivalent to the W3 extended conformal field theory. By considering the bulk scalar field as the operator in the W3 extended conformal field theory, we find the clue to the difficulty. In this Thesis, we formulate the spin-3 gravity coupled to a scalar field in terms of the action integral. In the large central charge limit, the W3 algebra reduces to the SU(1,2) algebra. By using this algebra, the state of the bulk scalar is constructed. The commutator [Wn,Wm] gives the Virasoro generator Ln+m, and in order to formulate the SU(1,2) invariant theory, it is necessary to introduce an enlarged spacetime by introducing five auxiliary coordinates as in the case of the supersymmetry. When the scalar field exists, half of SU(1,2) invariance is broken. The remaining invariance gives equations, which determine the state of the scalar. The state is an eigenstate of the quadratic Casimir operator of SU(1,2) algebra. The eigenvalue equation is interpreted as the equation of motion for free scalar in the eight-dimensional enlarged spacetime. The action integral is given by the one for the free scalar in the enlarged spacetime. Further, it is shown that the standard AdS/CFT dictionaries hold. The action integral for gravity is also studied. The scalar state is eigenstates of the cubic Casimir operator as well as the quadratic Casimir operator. The metric and the spin-3 gauge field are uniquely determined from the differential equations associated with the Casimir operators. It turns out that these fields are expressed in terms of SL(3,R) gauge connections.
Conffering University: 北海道大学
Degree Report Number: 甲第13563号
Degree Level: 博士
Degree Discipline: 理学
Examination Committee Members: (主査) 准教授 中山 隆一, 教授 鈴木 久男, 教授 小林 達夫, 講師 末廣 一彦
Degree Affiliation: 理学院(宇宙理学専攻)
Type: theses (doctoral)
URI: http://hdl.handle.net/2115/74291
Appears in Collections:課程博士 (Doctorate by way of Advanced Course) > 理学院(Graduate School of Science)
学位論文 (Theses) > 博士 (理学)

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