Motivated by the usual D2-D0 system, we consider a configuration composed of flat membrane and fuzzy sphere membrane in plane-wave matrix model, and investigate the interaction between them. The configuration is shown to lead to a non-trivial interaction potential, which indicates that the fuzzy sphere membrane really behaves like a graviton, giant graviton. Interestingly, the interaction is of r^{-3} type rather than r^{-5} type. We interpret it as the interaction incorporating the smearing effect due to the fact that the considered supersymmetric flat membrane should span and spin in four dimensional subspace of plane-wave geometry.
We investigate the interaction between flat membrane and point-like graviton in the plane-wave matrix model. The one-loop effective potential in the large distance limit is computed and is shown to be of r^{-3} type where r is the distance between two objects. This type of interaction has been interpreted as the one incorporating the smearing effect due to the configuration of flat membrane in plane-wave background. Our result supports this interpretation and provides one more evidence about it.
N=4 Supersymmetric Yang-Mills on S^3 in Plane Wave Matrix Model at Finite Temperature
通过平面波矩阵模型研究了弯曲时空中规范理论的大N约化模型。在大N极限下，我们从平面波矩阵模型正式推导出N=4超对称杨-米尔斯理论对R \times S ^3的作用量。此外，我们评估的有效行动的平面波矩阵模型的两个回路的水平在有限的温度。我们发现，在平面贡献占主导地位的高温极限下，有效作用量与S^3上N=4超对称杨-米尔斯理论的自由能是一致的。我们得出结论，平面波矩阵模型可以作为一个大N约化模型来研究R \times S ^[3]上N=4超对称杨-米尔斯理论的非微扰性质。
We consider matrix theoretical description of transverse M5-branes in M-theory on the 11-dimensional maximally supersymmetric pp-wave background. We apply the localization to the plane wave matrix model (PWMM) and show that the transverse spherical fivebranes with zero light cone energy in M-theory are realized as the distribution of low energy moduli of the $SO(6)$ scalar fields in PWMM.
The gravity dual geometry of the plane wave matrix model is given by the bubbling geometry in the type IIA supergravity, which is described by an axially symmetric electrostatic system. We study a quarter BPS sector of the plane wave matrix model in terms of the localization method and show that this sector can be mapped to a one-dimensional interacting Fermi gas system. We find that the mean-field density of the Fermi gas can be identified with the charge density in the electrostatic system in the gravity side. We also find that the scaling limits in which the dual geometry reduces to the D2-…
Derivation of the NS5-brane limit of the plane wave matrix model
Graduate School of Science and Technology, University of Tsukuba（筑波大学科学技术研究院）；Tomonaga Center for the History of the Universe, University of Tsukuba（筑波大学朝永宇宙史研究中心）
We perform a numerical simulation of the classical evolution of the plane-wave matrix model with semiclassical initial conditions. Some of these initial conditions thermalize and are dual to a black hole forming from the collision of D-branes in the plane wave geometry. In particular, we consider a large fuzzy sphere (a D2-brane) plus a single eigenvalue (a D0-particle) going exactly through the center of the fuzzy sphere and aimed to intersect it. Including quantum fluctuations of the off-diagonal modes in the initial conditions, with sufficient kinetic energy the configuration collapses to a…
We study the spacetime structures which are described by the IIB matrix model with orientifolding. Matrix orientifolding that preserves supersymmetries yields the mirror image point with respect to a four-dimensional plane for each spacetime point that corresponds to the eigenvalue of the bosonic matrix. In order to consider the upper bound on the distance between two eigenvalues in this model, we calculate the effective action for the eigenvalues up to two-loop. The eigenvalues distribute in a tubular region around the four-dimensional plane.
Zero-mode Spectrum of Eleven-dimensional Theory on the Plane-wave Background
在这篇博士论文中，我们研究了平面波背景下矩阵理论和十一维超引力的零模谱。该背景通过AdS_4 x S^7和AdS_7 x S^4的彭罗斯极限获得。平面波背景是一个极大的超对称时空，由11维时空中的非零常数四形式通量支持。首先，我们讨论了Berenstein，Maldacena和Nastase提出的平面波背景下的矩阵理论。构造了哈密顿量、32个超荷及其对易关系。我们讨论了一个特定的超多重态的频谱，它代表了质心自由度的ND 0-膜。这个超多重态也代表了在大N极限下的11维超引力的超粒子。其次，我们研究了十一维平面波背景下的线性超引力。将玻色子场和费米子场固定在光锥规范中，得到了物理模的谱。得到了矩阵理论中态的能量与超引力场的能量完全对应的事实。这样，我们发现平面波背景下的矩阵理论完全包含了11维超引力的零模谱。通过这个结果，我们可以论证平面波上的矩阵理论是十一维超引力量子扩展的候选者，或者是描述M理论的候选者。
We analyse two issues that arise in the context of (matrix) string theories in plane wave backgrounds, namely (1) the use of Brinkmann- versus Rosen-variables in the quantum theory for general plane waves (which we settle conclusively in favour of Brinkmann variables), and (2) the regularisation of the quantum dynamics for a certain class of singular plane waves (discussing the benefits and limitations of regularisations of the plane-wave metric itself).
We construct a matrix model equivalent (exactly, not asymptotically), to the random plane partition model, with almost arbitrary boundary conditions. Equivalently, it is also a random matrix model for a TASEP-like process with arbitrary boundary conditions. Using the known solution of matrix models, this method allows to find the large size asymptotic expansion of plane partitions, to ALL orders. It also allows to describe several universal regimes.
Field theories on the Groenewold-Moyal(GM) plane are studied using the Lehmann-Symanzik-Zimmermann(LSZ) formalism. The example of real scalar fields is treated in detail. The S-matrix elements in this non-perturbative approach are shown to be equal to the interaction representation S-matrix elements. This is a new non-trivial result: in both cases, the S-operator is independent of the noncommutative deformation parameter $θ_{μν}$ and the change in scattering amplitudes due to noncommutativity is just a time delay. This result is verified in two different ways. But the off-shell Green's functio…
We propose an alternative variational principle whose critical point is the algebraic plane curve associated to a matrix model (the spectral curve, i.e. the large $N$ limit of the resolvent). More generally, we consider a variational principle that is equivalent to the problem of finding a plane curve with given asymptotics and given cycle integrals. This variational principle is not given by extremization of the energy, but by the extremization of an "entropy".
We study the parameter dependence of the internal structure of resonance states by formulating Complex two-dimensional (2D) Matrix Model, where the two dimensions represent two-levels of resonances. We calculate a critical value of the parameter at which "nature transition" with character exchange occurs between two resonance states, from the viewpoint of geometry on complex-parameter space. Such critical value is useful to know the internal structure of resonance states with variation of the parameter in the system. We apply the model to analyze the internal structure of hadrons with variatio…
