Sharif Digital Repository

The tiny graviton Matrix theory [1] is proposed to describe DLCQ of type IIB string theory on the maximally supersymmetric plane-wave or AdS5 × S5 background. In this paper we provide further evidence in support of the tiny graviton conjecture by focusing on the zero energy, half BPS configurations of this matrix theory and classify all of them. These vacua are generically of the form of various three sphere giant gravitons. We clarify the connection between our solutions and the half BPS configuration in script N sign = 4 SYM theory and their gravity duals. Moreover, using our half BPS solutions, we show how the tiny graviton Matrix theory and the mass deformed D = 3,script N sign = 8... 

Near Horizon Extremal Geometries (NHEG) are solutions to gravity theories with SL(2, ℝ) × U(1) N (for some N) symmetry, are smooth geometries and have no event horizon, unlike black holes. Following the ideas by R. M. Wald, we derive laws of NHEG dynamics, the analogs of laws of black hole dynamics for the NHEG. Despite the absence of horizon in the NHEG, one may associate an entropy to the NHEG, as a Noether-Wald conserved charge. We work out "entropy" and "entropy perturbation" laws, which are respectively universal relations between conserved Noether charges corresponding to the NHEG and a system probing the NHEG. Our entropy law is closely related to Sen's entropy function. We also... 

We apply the Dirac bracket quantization to open strings attached to branes in the presence of background antisymmetric field and recover an inherent noncommutativity in the internal coordinates of the brane. © 2000 Elsevier Science B.V. All rights reserved  

In this paper the tachyonic resonance preheating generated from the bosonic trilinear χ2 interactions in an expanding universe is studied. In λ 4/4 inflationary model the trilinear interaction, in contrast to the four-legs 2χ2, breaks the conformal symmetry explicitly and the resonant source term becomes nonperiodic, making the Floquet theorem inapplicable. We find that the occupation number of the produced χ particles has a nonlinear exponential growth with exponent ∼x3/2, where x is the conformal time. This should be contrasted with preheating from a periodic resonant source arising, for example, from the four-legs 2χ2 interaction, where the occupation number has a linear exponential... 

We construct the NHEG phase space, the classical phase space of Near-Horizon Extremal Geometries with fixed angular momenta and entropy, and with the largest symmetry algebra. We focus on vacuum solutions to d dimensional Einstein gravity. Each element in the phase space is a geometry with SL(2,R)×U(1)d-3 isometries which has vanishing SL(2,R) and constant U(1) charges. We construct an on-shell vanishing symplectic structure, which leads to an infinite set of symplectic symmetries. In four spacetime dimensions, the phase space is unique and the symmetry algebra consists of the familiar Virasoro algebra, while in d> 4 dimensions the symmetry algebra, the NHEG algebra, contains infinitely many... 

Abstract: We construct the classical phase space of geometries in the near-horizon region of vacuum extremal black holes as announced in [arXiv:1503.07861]. Motivated by the uniqueness theorems for such solutions and for perturbations around them, we build a family of metrics depending upon a single periodic function defined on the torus spanned by the U(1) isometry directions. We show that this set of metrics is equipped with a consistent symplectic structure and hence defines a phase space. The phase space forms a representation of an infinite dimensional algebra of so-called symplectic symmetries. The symmetry algebra is an extension of the Virasoro algebra whose central extension is the... 

We extend the analysis of Fareghbal to charged black hole solutions of four-dimensional U(1)4 gauged supergravity which carry three charges. There are two decoupling near-horizon limits, one over the near-Bogomol'nyi-Prasad- Sommerfield (BPS) black hole solution and the other over the near-extremal, but non-BPS geometry. Taking the limit over the 11-dimensional uplift of these black hole solutions, for both of these cases we obtain a geometry which has a piece (conformal) to rotating BTZ×S2. We study the 4D, 11D, and 5D, 3D black hole properties. Moreover, we show that the BTZ×S2 geometry obtained after the near-BPS (near-extremal) limit is also a solution to five-dimensional U(1)3 ungauged... 

We study near-horizon limits of near-extremal charged black hole solutions to five-dimensional U(1) 3 gauged supergravity carrying two charges, extending the recent work of Balasubramanian et al. [1]. We show that there are two near-horizon decoupling limits for the near-extremal black holes, one corresponding to the near-BPS case and the other for the far from BPS case. Both of these limits are only defined on the 10d IIB uplift of the 5d black holes, resulting in a decoupled geometry with a six-dimensional part (conformal to) a rotating BTZ × S 3. We study various aspects of these decoupling limits both from the gravity side and the dual field theory side. For the latter we argue that... 

We consider D3-brane action in the maximally supersymmetric type IIB plane-wave background. Upon fixing the light-cone gauge, we obtain the light-cone Hamiltonian which is manifestly supersymmetric. The 1/2 BPS solutions of this theory (solutions which preserve 16 supercharges) are either of the form of spherical three branes, the giant gravitons, or zero size point like branes. We then construct specific classes of 1/4 BPS solutions of this theory in which static electric field on the brane is turned on. These solutions are deformations about either of the two 1/2 BPS solutions. In particular, we study in some detail 1/4 BPS configurations with electric dipole on the three sphere giant,... 

In this paper, the general solution of steady-state 1D radially symmetric mechanical and thermal stresses and electrical and mechanical displacements for a hollow thick cylinder made of fluid-saturated functionally graded poro piezoelectric materials (FGPPMs) is developed. The general form of thermal and mechanical boundary conditions is considered on the inside and outside surfaces. A direct method is used to solve the heat conduction equation and nonhomogenous system of partial differential Navier equations, using complex Fourier series and power law functions method. The material properties, except the Poisson ratio, are assumed to depend on the radial variable r and they are expressed as... 

We consider single field chaotic inflationary models plus a cosine modulation term, as in axion monodromy models, and augment them by a light scalar field with similar cosine coupling. We show that the power spectrum of curvature perturbations of this model is dominated by the one-loop contribution to the inflaton two-point function which is enhanced due to resonant interactions. This allows us to disentangle the scale of the scalar and tensor perturbations and hence, to suppress the ratio of tensor-to-scalar power spectra and alter the expression of the scalar spectral tilt from the simple chaotic models. Thus, our resonating module opens the way to reconcile chaotic models with convex... 

Expanding on [1], we analyze in detail the single field chaotic inflationary models plus a cosine modulation term, augmented by a light scalar field with inflaton dependent oscillatory mass term. We work out in detail the Feynman diagrams and compute one, two and in general estimate higher loop two and three point functions in the in-in formulation. We explicitly establish how the oscillatory mass term can amplify one-loop effects to dominate over the tree as well as the higher loop contributions. The power spectrum of curvature perturbations of this model is hence enhanced compared to the simple single field chaotic model. As a consequence, one can suppress the tensor to scalar ratio r and... 

In this paper we continue analysis of the Matrix theory describing the DLCQ of type IIB string theory on AdS5×S5 (and/or the plane-wave) background, i.e. the tiny graviton matrix theory (TGMT). We study and classify 1/2, 1/4, and 1/8 BPS solutions of the TGMT which are generically of the form of rotating three-brane giants. These are branes whose shape are deformed three-spheres and hyperboloids. In lack of a classification of such ten-dimensional type IIb supergravity configurations, we focus on the dual N=4 four-dimensional 1/2, 1/4, and one 1/8 BPS operators and show that they are in one-to-one correspondence with the states of the same set of quantum numbers in TGMT. This provides... 

In this paper we consider all consistent extensions of the AdS5 × S5 superalgebra, psu(2,2/4), to incorporate brane charges by introducing both bosonic and fermionic (non)central extensions. We study the Inönü-Wigner contraction of the extended psu(2,2/4) under the Penrose limit to obtain the most general consistent extension of the plane-wave superalgebra and compare these extensions with the possible BPS (flat or spherical) brane configurations in the plane-wave background. We give an explicit realization of some of these extensions in terms of the Tiny Graviton Matrix Theory (TGMT) [14] which is the 0+1 dimensional gauge theory conjectured to describe the DLCQ of strings on the AdS5 × S5... 

This paper develops an approach to determine the optimal production and shipment policy for an integrated vendor-buyer problem. The vendor manufactures the product in batches at a finite rate and ships the output to the buyer. All shipments to the buyer are equal-sized batches. Despite previous papers in the literature, we assume that the supply lead-time between vendor and buyer is stochastic and shortage is also allowed. The objective is to minimize the expected total cost of both buyer and vendor. We derive the expected annual integrated total cost function and propose an analytic solution procedure to determine the optimal policy. To illustrate the significance of cost-reduction of the...