@misc{oai:ir.soken.ac.jp:00004067,
author = {本多, 正純 and ホンダ, マサズミ and HONDA, Masazumi},
month = {2016-02-26, 2016-02-17},
note = {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<