Macroscopic Black Holes, Microscopic Black Holes and Noncommutative Membrane

We study the stretched membrane of a black hole as consisting of a perfect fluid. We find that the pressure of this fluid is negative and the specific heat is negative too. A surprising result is that if we are to assume the fluid be composed of some quanta, then the dispersion relation of the fundamental quantum is $E=m^2/k$, with $m$ at the scale of the Planck mass. There are two possible interpretation of this dispersion relation, one is the noncommutative spacetime on the stretched membrane, another is that the fundamental quantum is microscopic black holes.Comment: 10 pages, harvmac; v2: refs. adde

Generalized Conformal Symmetry and Oblique AdS/CFT Correspondence for Matrix Theory

The large N behavior of Matrix theory is discussed on the basis of the previously proposed generalized conformal symmetry. The concept of `oblique' AdS/CFT correspondence, in which the conformal symmetry involves both the space-time coordinates and the string coupling constant, is proposed. Based on the explicit predictions for two-point correlators, possible implications for the Matrix-theory conjecture are discussed.Comment: LaTeX, 10 pages, 2 figures, written version of the talk presented at Strings'9

Generalized Conformal Symmetry in D-Brane Matrix Models

We study in detail the extension of the generalized conformal symmetry proposed previously for D-particles to the case of supersymmetric Yang-Mills matrix models of Dp-branes for arbitrary p. It is demonstrated that such a symmetry indeed exists both in the Yang-Mills theory and in the corresponding supergravity backgrounds produced by Dp-branes. On the Yang-Mills side, we derive the field-dependent special conformal transformations for the collective coordinates of Dp-branes in the one-loop approximation, and show that they coincide with the transformations on the supergravity side. These transformations are powerful in restricting the forms of the effective actions of probe D-branes in the fixed backgrounds of source D-branes. Furthermore, our formalism enables us to extend the concept of (generalized) conformal symmetry to arbitrary configurations of D-branes, which can still be used to restrict the dynamics of D-branes. For such general configurations, however, it cannot be endowed a simple classical space-time interpretation at least in the static gauge adopted in the present formulation of D-branes.Comment: 26 pages, no figure

Quantum Metamorphosis of Conformal Transformation in D3-Brane Yang-Mills Theory

We show how the linear special conformal transformation in four-dimensional N=4 super Yang-Mills theory is metamorphosed into the nonlinear and field-dependent transformation for the collective coordinates of Dirichlet 3-branes, which agrees with the transformation law for the space-time coordinates in the anti-de Sitter (AdS) space-time. Our result provides a new and strong support for the conjectured relation between AdS supergravity and super conformal Yang-Mills theory (SYM). Furthermore, our work sheds elucidating light on the nature of the AdS/SYM correspondence.Comment: 8 pages, no figure

On the Bekenstein-Hawking Entropy, Non-Commutative Branes and Logarithmic Corrections

We extend earlier work on the origin of the Bekenstein-Hawking entropy to higher-dimensional spacetimes. The mechanism of counting states is shown to work for all spacetimes associated with a Euclidean doublet $(E_1,M_1)+(E_2,M_2)$ of electric-magnetic dual brane pairs of type II string-theory or M-theory wrapping the spacetime's event horizon plus the complete internal compactification space. Non-Commutativity on the brane worldvolume enters the derivation of the Bekenstein-Hawking entropy in a natural way. Moreover, a logarithmic entropy correction with prefactor 1/2 is derived.Comment: 17 pages, 2 figures; refs. adde

Noncommutative models in patch cosmology

We consider several classes of noncommutative inflationary models within an extended version of patch cosmological braneworlds, starting from a maximally invariant generalization of the action for scalar and tensor perturbations to a noncommutative brane embedded in a commutative bulk. Slow-roll expressions and consistency relations for the cosmological observables are provided, both in the UV and IR region of the spectrum; the inflaton field is assumed to be either an ordinary scalar field or a Born-Infeld tachyon. The effects of noncommutativity are then analyzed in a number of ways and energy regimes.Comment: 13 pages, 8 figures. Figures 1 and 2 are included in the text, Figs. 3-8 are in a low-resolution jpeg format. These and other high-resolution figures are available upon request to the author ([email protected]). v3: corrected misprint

Generalized Uncertainty Principle, Modified Dispersion Relations and Early Universe Thermodynamics

In this paper, we study the effects of Generalized Uncertainty Principle(GUP) and Modified Dispersion Relations(MDRs) on the thermodynamics of ultra-relativistic particles in early universe. We show that limitations imposed by GUP and particle horizon on the measurement processes, lead to certain modifications of early universe thermodynamics.Comment: 21 Pages, 3 eps Figure, Revised Versio

Solution of the dispersionless Hirota equations

The dispersionless differential Fay identity is shown to be equivalent to a kernel expansion providing a universal algebraic characterization and solution of the dispersionless Hirota equations. Some calculations based on D-bar data of the action are also indicated.Comment: Late

T-Duality Transformation and Universal Structure of Non-Critical String Field Theory

We discuss a T-duality transformation for the c=1/2 matrix model for the purpose of studying duality transformations in a possible toy example of nonperturbative frameworks of string theory. Our approach is to first investigate the scaling limit of the Schwinger-Dyson equations and the stochastic Hamiltonian in terms of the dual variables and then compare the results with those using the original spin variables. It is shown that the c=1/2 model in the scaling limit is T-duality symmetric in the sphere approximation. The duality symmetry is however violated when the higher-genus effects are taken into account, owing to the existence of global Z_2 vector fields corresponding to nontrivial homology cycles. Some universal properties of the stochastic Hamiltonians which play an important role in discussing the scaling limit and have been discussed in a previous work by the last two authors are refined in both the original and dual formulations. We also report a number of new explicit results for various amplitudes containing macroscopic loop operators.Comment: RevTex, 46 pages, 5 eps figure

Toda Lattice Hierarchy and Generalized String Equations

String equations of the $p$-th generalized Kontsevich model and the compactified $c = 1$ string theory are re-examined in the language of the Toda lattice hierarchy. As opposed to a hypothesis postulated in the literature, the generalized Kontsevich model at $p = -1$ does not coincide with the $c = 1$ string theory at self-dual radius. A broader family of solutions of the Toda lattice hierarchy including these models are constructed, and shown to satisfy generalized string equations. The status of a variety of $c \le 1$ string models is discussed in this new framework.Comment: 35pages, LaTeX Errors are corrected in Eqs. (2.21), (2.36), (2.33), (3.3), (5.10), (6.1), sentences after (3.19) and theorem 5. A few references are update