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Numerical test of AdS/CFT correspondence for M2-branes
https://ir.soken.ac.jp/records/4067
https://ir.soken.ac.jp/records/40672ed657a5-b863-427c-9199-a8bfa7bb48af
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要旨・審査要旨 (287.7 kB)
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本文 (1.7 MB)
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| Item type | 学位論文 / Thesis or Dissertation(1) | |||||||
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| 公開日 | 2013-11-15 | |||||||
| タイトル | ||||||||
| タイトル | Numerical test of AdS/CFT correspondence for M2-branes | |||||||
| タイトル | ||||||||
| タイトル | Numerical test of AdS/CFT correspondence for M2-branes | |||||||
| 言語 | en | |||||||
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| 言語 | eng | |||||||
| 資源タイプ | ||||||||
| 資源タイプ識別子 | http://purl.org/coar/resource_type/c_46ec | |||||||
| 資源タイプ | thesis | |||||||
| 著者名 |
本多, 正純
× 本多, 正純
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| フリガナ |
ホンダ, マサズミ
× ホンダ, マサズミ
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| 著者 |
HONDA, Masazumi
× HONDA, Masazumi
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| 学位授与機関 | ||||||||
| 学位授与機関名 | 総合研究大学院大学 | |||||||
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| 学位名 | 博士（理学） | |||||||
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| 内容記述タイプ | Other | |||||||
| 内容記述 | 総研大甲第1590号 | |||||||
| 研究科 | ||||||||
| 値 | 高エネルギー加速器科学研究科 | |||||||
| 専攻 | ||||||||
| 値 | 14 素粒子原子核専攻 | |||||||
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| 学位授与年月日 | 2013-03-22 | |||||||
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| 値 | 2012 | |||||||
| 要旨 | ||||||||
| 内容記述タイプ | Other | |||||||
| 内容記述 | Numerical test of AdS/CFT correspondence for M2-branes M-theory is an eleven-dimensional theory, which has been proposed as a strong coupling limit of the type IIA superstring theory. It has been also expected that the M-theory includes the eleven-dimensional supergravity (11d SUGRA) as a low-energy limit. The 11d SUGRA consists of the graviton, gravitino and three-form gauge field. The three-form field in eleven dimensions electrically (magnetically) couples to two(five)-dimensional object. Such objects naturally appear as black brane solutions conserving a part of supersymmetries in the 11d SUGRA. On the analogy of the relation between such solutions in the ten-dimensional supergravities and objects in the superstring theories as string, NS5-brane and D-branes, we can expect that the M-theory has fundamental two- and five-dimensional objects. These objects are called as ``M2-brane`` and ``M5-brane``, respectively. In this thesis, we focus on Physics of the multiple M2-branes. As well known, a low-energy limit of parallel N Dp-branes is described by the (p+1)-dimensional U(N) maximally supersymmetric Yang-Mills theory. This U(N) gauge symmetry can be intuitively understood by the facts that open string includes spin-1 massless boson in its spectrum and have an U(1) charge called as a Chan-Paton factor. What is a low-energy effective theory of the parallel N M2-branes? Unfortunately, we have not an established answer to this question yet as we will argue below. From the single M2-brane analysis and implication of the AdS/CFT correspondence, we expect that the low energy effective theory for $N$ M2-branes has the following properties: (1) Three dimensional conformal symmetry, (2) N=8 supersymmetry, (3) SO(8) R-symmetry, and so on. However, such a theory had not been found for long years. There are many reasons for this. One of most serious obstacle is difficulty of quantization of supermembrane. This prevents us from finding spectrum and something like a Chan-Paton factor for M2-branes. Another difficult -ty is that it is not easy to construct gauge theory with conformal and high supersymmetry except for four dimensions. Since Yang-Mills action is scale invariant only for four dimensionns, we can use only Chern-Simons term of vector multiplet and marginal term of chiral multiplet for the construction. Indeed in 1990's, a maximal supersymmetric extension of Chern- Simons theory had been N=3. In 2008, Aharony, Bergman, Jafferis and Maldacena (ABJM) has proposed a U(N)xU(N) theory with Chern-Simons levels k and -k coupled to bi-fundamental matters. This theory has N=8 supersymmetry for k=1,2 and N=6 supersymmetry for other values of k. It has been conjectured tobe dual to M-theory on AdS_4 x S^7/Z_k for k<<N^{1/5}, and to type IIA superstring onAdS_4xCP^3 in the planar large-N limit with the 't Hooft coupling constant λ=N/ k kept fixed. From the viewpoint of quantum gravity, the ABJM theory is important since it may provide us with a nonperturbative definition of type IIA superstring theory or M-theory on AdS_4 back-grounds since the theory is well-defined for finite N. One may draw a precise analogy with the way maximally supersymmetric Yang-Mills theories may provide us with non perturbative formulations of type IIA/IIB superstring theories on D-brane backgrounds through the gauge/gravity duality. In particular, the M-theory limit is important given that M-theory is not defined even perturbatively, although there is a well-known conjecture on its nonperturbative formulation in the infinite momentum frame in terms of matrix quantum mechanics. The planar limit, which corresponds to type IIA superstring theory, has interest on its own since it may allow us to perform more detailed tests of the gauge/gravity duality than in the case of AdS_5/CFT_4. In particular, we may hope to calculate the 1/N corrections to the planar limit, which enables us to test the gauge/gravity duality at the quantum string level, little of which is known so far. In all these prospectives, one needs to study the ABJM theory in the strong coupling regime. As in the case of QCD, it would be nice if one could study the ABJM theory on a lattice by Monte Carlo methods. This seems quite difficult, though, for the following three reasons. Firstly, the construction of the Chern-Simons term on the lattice is not straightforward, although there is a proposal based on its connection to the parity anomaly. Secondly, the Chern-Simons term is purely imaginary in the Euclidean formulation, which causes a technical problem known as the sign problem when one tries to apply the idea of importance sampling. Thirdly, the lattice discretization necessarily breaks supersymmetry, and one needs to restore it in the continuum limit by fine-tuning the coupling constants of the supersymmetry breaking relevant operators. This might, however, be overcome by the use of a non-lattice regularization of the ABJM theory based on the large-N reduction on S^3, which is shown to be useful in studying the planar limit of the 4d N=4 super Yang-Mills theory. In this thesis, we show that the ABJM theory can be studied for arbitrary N at arbitrary cou pling constant by applying a simple Monte Carlo method to the matrix model that can be deri ved from the theory by using the localization technique. This opens up the possibility of probing the quantum aspects of M-theory and testing the AdS_4/CFT_3 duality at the quantum level. Here we calculate the free energy, and confirm the N^3/2 scaling in the M-theory limit predicted from the gravity side. We also find that our results nicely interpolate the analytical formulae proposed previously in the M-theory and type IIA regimes. Furthermore, we show that some results obtained by the Fermi gas approach can be clearly understood from the constant map contribution obtained by the genus expansion. The method can be easily generalized to the calculations of BPS operators and to other theories that reduce to matrix models. We also study the super-symmetric Wilson loops in the ABJM theory. Our result nicely interpolates the expressions at weak and strong coupling regions. |
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