Holography and D3-branes in Melvin Universes

Recently,in a paper hep-th/0511197, it was found that non-commutative super Yang-Mills (NCSYM) theory with space-dependent noncommutativity can be formulated as a decoupling limit of open strings ending on D3-branes wrapping a Melvin universe supported by a flux of the NSNS B-field. Under S-duality, we show that this theory turns into a noncommutative open string (NCOS) theory with space-dependent space-time noncommutativity and effective space-dependent string scale. It is an NCOS theory with both space-dependent space-space and space-time noncommutativities under more general $SL(2,\mathbb{Z})$ transformation. These space-dependent noncommutative theories (NCSYM and NCOS) have completely the same thermodynamics as that of ordinary super YM theory, NCSYM and NCOS theories with constant noncommutativity in the dual supergravity description. Starting from black D3-brane solution in the Melvin universe and making a Lorentz boost along one of spatial directions on the worldvolume of D3-branes, we show that the decoupled theory is a light-like NCSYM theory with space-dependent noncommutativity in a static frame or in an infinite-momentum frame depending on whether there is a gravitational pp-wave on the worldvolume of the D3-branes.Comment: Latex, 13 pages, v2: typos fixed, the version in PR

Bekenstein Bound, Holography and Brane Cosmology in Charged Black Hole Backgrounds

We obtain a Bekenstein entropy bound for the charged objects in arbitrary dimensions ($D\ge 4$) using the D-bound recently proposed by Bousso. With the help of thermodynamics of CFTs corresponding to AdS Reissner-Norstr\"om (RN) black holes, we discuss the relation between the Bekenstein and Bekenstein-Verlinde bounds. In particular we propose a Bekenstein-Verlinde-like bound for the charged systems. In the Einstein-Maxwell theory with a negative cosmological constant, we discuss the brane cosmology with positive tension using the Binetruy-Deffayet-Langlois approach. The resulting Friedman-Robertson-Walker equation can be identified with the one obtained by the moving domain wall approach in the AdS RN black hole background. Finally we also address the holographic property of the brane universe.Comment: Latex, 17 pages, v2: minor changes, a reference adde

On the local term in the anomaly-induced action of Weyl quantum gravity

The finite local conformally non-invariant $R^2$-term emerges in the one-loop effective action of the model of quantum gravity based on the Weyl-squared classical action. This term is related to the $\Box R$ contribution to the conformal anomaly, which in a wide class of regularization schemes is determined by the second Schwinger-DeWitt (or Gilkey-Seeley) coefficient of the heat kernel expansion for inverse propagators of the theory. The calculation of this term requires evaluating the contributions of the fourth-order derivative minimal and of the second-order nonminimal operators in the tensor and vector sectors of the theory, corresponding to metric, ghost and gauge-fixing operators. To ensure the correctness of existing formulas, we derived (and confirmed) the result using a special technique of calculations, based on the heat-kernel representation of the Euclidean Green's function and the method of universal functional traces.Comment: 30 page

Deconfinement Transition of AdS/QCD at O(α′3){\cal O}(\alpha'^3)

We study the confinement/deconfinement phase transition of holographic AdS/QCD models by using Ricci flat $AdS_5$ black holes up to ${\cal O}(\alpha'^3)$, which corresponds to the $\lambda$ expansion correction in the dual field theory to $\lambda^{-3/2}$, where $\lambda$ is the 't Hooft coupling constant. We consider two cases: one is the hard-wall AdS/QCD model where a small radius region of the $AdS_5$ is removed; the other is the case where one of spatial coordinates for the $AdS_5$ space is compactified, resulting in Witten's QCD model in 2+1 dimensions. We find that in the hard-wall AdS/QCD model, the deconfinement temperature decreases when the $\lambda$ expansion corrections are taken into account, while in Witten's QCD model, the deconfinement transition always happens when the ratio of inverse temperature $\beta$ to the period $\beta_s$ of the compactified coordinate decreases to one, $\beta/\beta_s=1$, the same as the case without the ${\cal O}(\alpha'^3)$ correction.Comment: Latex, 14 pages; v2: the version to appear in PR

The BRST Operator for the Large N=4N=4 Superconformal Algebra

We review the detailed structure of the large $N=4$ superconformal algebra, and construct its BRST operator which constitutes the main object for analyzing $N=4$ strings. We then derive the general condition for the nilpotency of the BRST operator and show that there exists a line of critical $N=4$ string theories.Comment: Latex file, 16 pages, NBI-HE-94-1

A Complete Classification of Higher Derivative Gravity in 3D and Criticality in 4D

We study the condition that the theory is unitary and stable in three-dimensional gravity with most general quadratic curvature, Lorentz-Chern-Simons and cosmological terms. We provide the complete classification of the unitary theories around flat Minkowski and (anti-)de Sitter spacetimes. The analysis is performed by examining the quadratic fluctuations around these classical vacua. We also discuss how to understand critical condition for four-dimensional theories at the Lagrangian level.Comment: 20 pages, v2: minor corrections, refs. added, v3: logic modified, v4: typos correcte

A Hierarchy of Superstrings

We construct a hierarchy of supersymmetric string theories by showing that the general N-extended superstrings may be viewed as a special class of the (N+1)-extended superstrings. As a side result, we find a twisted (N+2) superconformal algebra realized in the N-extended string.Comment: 9 pages, LaTex, NBI-HE-94-2

Dynamics of intersecting brane systems -- Classification and their applications --

We present dynamical intersecting brane solutions in higher-dimensional gravitational theory coupled to dilaton and several forms. Assuming the forms of metric, form fields, and dilaton field, we give a complete classification of dynamical intersecting brane solutions with/without M-waves and Kaluza-Klein monopoles in eleven-dimensional supergravity. We apply these solutions to cosmology and black holes. It is shown that these give FRW cosmological solutions and in some cases Lorentz invariance is broken in our world. If we regard the bulk space as our universe, we may interpret them as black holes in the expanding universe. We also discuss lower-dimensional effective theories and point out naive effective theories may give us some solutions which are inconsistent with the higher-dimensional Einstein equations.Comment: 44 pages; v2: minor corrections, references adde

Spacetime Superalgebra in AdS_4 \times S^7 via Supermembrane Probe

The spacetime superalgebra via the supermembrane probe in the background of AdS_4 \times S^7 is discussed to the lowest order in the spinor coordinate \t. To obtain the correct spacetime superalgebras, all \t^2 order corrections for supervielbein and super 3-form gauge potential have to be included. The central extension of the superalgebra OSp(8|4) of the super isometries for AdS_4 \times S^7 is found.Comment: 8 pages, Latex, minor corrections, final version to appear in Phys. Rev.