Abstract:In this paper, we study the half-supersymmetric time-dependent configurations in M-theory and their matrix models. We find a large class of 11D supergravity solutions, which keeps sixteen supersymmetries. Furthermore, we investigate the isometries of these configurations and show that in general these configurations have no supernumerary supersymmetry. And also we define the matrix models in these backgrounds following Discrete Light-Cone Quantization (DLCQ) prescription. *
“…The essential point is that the Fock space of this theory is defined in terms of creation and annihilation operators coming from the usual mode expansion ofφ. If we had started instead with an interacting theory with action, 27) then after changing toφ variables and dropping a surface term, the resulting action is,…”
Section: The Sym Theory In the Presence Of A Varying Dilatonmentioning
We investigate backgrounds of Type IIB string theory with null singularities and their duals proposed in hep-th/0602107. The dual theory is a deformed N = 4 Yang-Mills theory in 3+1 dimensions with couplings dependent on a light-like direction. We concentrate on backgrounds which become AdS 5 × S 5 at early and late times and where the string coupling is bounded, vanishing at the singularity. Our main conclusion is that in these cases the dual gauge theory is nonsingular. We show this by arguing that there exists a complete set of gauge invariant observables in the dual gauge theory whose correlation functions are nonsingular at all times. The two-point correlator for some operators calculated in the gauge theory does not agree with the result from the bulk supergravity solution. However, the bulk calculation is invalid near the singularity where corrections to the supergravity approximation become important. We also obtain pp-waves which are suitable Penrose limits of this general class of solutions, and construct the Matrix Membrane theory which describes these pp-wave backgrounds.
“…The essential point is that the Fock space of this theory is defined in terms of creation and annihilation operators coming from the usual mode expansion ofφ. If we had started instead with an interacting theory with action, 27) then after changing toφ variables and dropping a surface term, the resulting action is,…”
Section: The Sym Theory In the Presence Of A Varying Dilatonmentioning
We investigate backgrounds of Type IIB string theory with null singularities and their duals proposed in hep-th/0602107. The dual theory is a deformed N = 4 Yang-Mills theory in 3+1 dimensions with couplings dependent on a light-like direction. We concentrate on backgrounds which become AdS 5 × S 5 at early and late times and where the string coupling is bounded, vanishing at the singularity. Our main conclusion is that in these cases the dual gauge theory is nonsingular. We show this by arguing that there exists a complete set of gauge invariant observables in the dual gauge theory whose correlation functions are nonsingular at all times. The two-point correlator for some operators calculated in the gauge theory does not agree with the result from the bulk supergravity solution. However, the bulk calculation is invalid near the singularity where corrections to the supergravity approximation become important. We also obtain pp-waves which are suitable Penrose limits of this general class of solutions, and construct the Matrix Membrane theory which describes these pp-wave backgrounds.
“…Some previous attempts at studying time dependent phenomena pertaining to cosmological singularities in string theory include e.g. [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31].…”
We construct a family of solutions in IIB supergravity theory. These are time dependent or depend on a light-like coordinate and can be thought of as deformations of AdS 5 × S 5 . Several of the solutions have singularities. The light-like solutions preserve 8 supersymmetries. We argue that these solutions are dual to the N = 4 gauge theory in a 3 + 1 dimensional spacetime with a metric and a gauge coupling that is varying with time or the light-like direction respectively. This identification allows us to map the question of singularity resolution to the dual gauge theory.
“…Since lim τ →−∞ λ = ∞ in this case, the large spatial extension reduce fuzzy effect. This phenomenon happens also in the matrix models on other timedependent backgrounds [8,24].…”
Section: The Fuzzy Three Sphere Solutionsmentioning
confidence: 72%
“…For the general curved spacetime, the action of the supermembrane could not be determined completely [7]. However, it is remarkable, for a general class of plane-wave-like background, the matrix model could be constructed to all order [8].…”
In this article we construct a tiny graviton matrix model for type IIB string theory on a plane-wave background with null dilaton. For the linear null dilaton case, we analyze its vacuum and the excitation spectrum around the vacuum, and discuss the time-dependent fuzzy three-sphere solutions and their evolution. It turns out that at very late time the non-Abelian fuzzy degrees of freedom disappear, which indicates the appearance of perturbative strings. *
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