Effective dimensions and percolation in hierarchically structured scale-free networks

We introduce appropriate definitions of dimensions in order to characterize the fractal properties of complex networks. We compute these dimensions in a hierarchically structured network of particular interest. In spite of the nontrivial character of this network that displays scale-free connectivity among other features, it turns out to be approximately one-dimensional. The dimensional characterization is in agreement with the results on statistics of site percolation and other dynamical processes implemented on such a network.Comment: 5 pages, 5 figure

Poisson Algebra of Diffeomorphism Generators in a Spacetime Containing a Bifurcation

In this article we will analyze the possibility of a nontrivial central extension of the Poisson algebra of the diffeomorphism generators, which respect certain boundary conditions on the black hole bifurcation. The origin of a possible central extension in the algebra is due to the existence of boundary terms in the in the canonical generators. The existence of such boundary terms depend on the exact boundary conditions one takes. We will check two possible boundary conditions i.e. fixed bolt metric and fixed surface gravity. In the case of fixed metric the the action acquires a boundary term associated to the bifurcation but this is canceled in the Legendre transformation and so absent in the canonical generator and so in this case the possibility of a nontrivial central extension is ruled out. In the case of fixed surface gravity the boundary term in the action is absent but present in the Hamiltonian. Also in this case we will see that there is no nontrivial central extension, also if there exist a boundary term in the generator.Comment: LaTex 20 pages, some misprints corrected, 2 references added. Accepted for publication on Phys. Rev.

Prepotential and Instanton Corrections in N=2 Supersymmetric SU(N_1)xSU(N_2) Yang Mills Theories

In this paper we analyse the non-hyperelliptic Seiberg-Witten curves derived from M-theory that encode the low energy solution of N=2 supersymmetric theories with product gauge groups. We consider the case of a SU(N_1)xSU(N_2) gauge theory with a hypermultiplet in the bifundamental representation together with matter in the fundamental representations of SU(N_1) and SU(N_2). By means of the Riemann bilinear relations that hold on the Riemann surface defined by the Seiberg--Witten curve, we compute the logarithmic derivative of the prepotential with respect to the quantum scales of both gauge groups. As an application we develop a method to compute recursively the instanton corrections to the prepotential in a straightforward way. We present explicit formulas for up to third order on both quantum scales. Furthermore, we extend those results to SU(N) gauge theories with a matter hypermultiplet in the symmetric and antisymmetric representation. We also present some non-trivial checks of our results.Comment: 21 pages, 2 figures, minor changes and references adde

Effective superpotential for U(N) with antisymmetric matter

We consider an N=1 U(N) gauge theory with matter in the antisymmetric representation and its conjugate, with a tree level superpotential containing at least quartic interactions for these fields. We obtain the effective glueball superpotential in the classically unbroken case, and show that it has a non-trivial N-dependence which does not factorize. We also recover additional contributions starting at order S^N from the dynamics of Sp(0) factors. This can also be understood by a precise map of this theory to an Sp(2N-2) gauge theory with antisymmetric matter.Comment: 22 pages. v2: comment (and a reference) added at the end of section 2 on low rank cases; minor typos corrected. v3: 2 footnotes added with additional clarifications; version to appear in journa

Chiral field theories from conifolds

We discuss the geometric engineering and large n transition for an N=1 U(n) chiral gauge theory with one adjoint, one conjugate symmetric, one antisymmetric and eight fundamental chiral multiplets. Our IIB realization involves an orientifold of a non-compact Calabi-Yau A_2 fibration, together with D5-branes wrapping the exceptional curves of its resolution as well as the orientifold fixed locus. We give a detailed discussion of this background and of its relation to the Hanany-Witten realization of the same theory. In particular, we argue that the T-duality relating the two constructions maps the Z_2 orientifold of the Hanany-Witten realization into a Z_4 orientifold in type IIB. We also discuss the related engineering of theories with SO/Sp gauge groups and symmetric or antisymmetric matter.Comment: 34 pages, 8 figures, v2: References added, minor correction

Chiral rings, anomalies and loop equations in N=1* gauge theories

We examine the equivalence between the Konishi anomaly equations and the matrix model loop equations in N=1* gauge theories, the mass deformation of N=4 supersymmetric Yang-Mills. We perform the superfunctional integral of two adjoint chiral superfields to obtain an effective N=1 theory of the third adjoint chiral superfield. By choosing an appropriate holomorphic variation, the Konishi anomaly equations correctly reproduce the loop equations in the corresponding three-matrix model. We write down the field theory loop equations explicitly by using a noncommutative product of resolvents peculiar to N=1* theories. The field theory resolvents are identified with those in the matrix model in the same manner as for the generic N=1 gauge theories. We cover all the classical gauge groups. In SO/Sp cases, both the one-loop holomorphic potential and the Konishi anomaly term involve twisting of index loops to change a one-loop oriented diagram to an unoriented diagram. The field theory loop equations for these cases show certain inhomogeneous terms suggesting the matrix model loop equations for the RP2 resolvent.Comment: 23 pages, 3 figures, latex2e, v4: minor changes in introduction and conclusions, 4 references are added, version to appear in JHE

The Asymptotic Dynamics of two-dimensional (anti-)de Sitter Gravity

We show that the asymptotic dynamics of two-dimensional de Sitter or anti-de Sitter Jackiw-Teitelboim (JT) gravity is described by a generalized two-particle Calogero-Sutherland model. This correspondence is established by formulating the JT model of (A)dS gravity in two dimensions as a topological gauge theory, which reduces to a nonlinear 0+1-dimensional sigma model on the boundary of (A)dS space. The appearance of cyclic coordinates allows then a further reduction to the Calogero-Sutherland quantum mechanical model.Comment: 16 pages, LaTeX, no figures, uses JHEP.cls. v2: Some references and comments added. v3: Minor errors correcte

The Fall of Stringy de Sitter

Kachru, Kallosh, Linde, & Trivedi recently constructed a four-dimensional de Sitter compactification of IIB string theory, which they showed to be metastable in agreement with general arguments about de Sitter spacetimes in quantum gravity. In this paper, we describe how discrete flux choices lead to a closely-spaced set of vacua and explore various decay channels. We find that in many situations NS5-brane meditated decays which exchange NSNS 3-form flux for D3-branes are comparatively very fast.Comment: 35 pp (11 pp appendices), 5 figures, v3. fixed minor typo

Exact scaling properties of a hierarchical network model

We report on exact results for the degree $K$, the diameter $D$, the clustering coefficient $C$, and the betweenness centrality $B$ of a hierarchical network model with a replication factor $M$. Such quantities are calculated exactly with the help of recursion relations. Using the results, we show that (i) the degree distribution follows a power law $P_K \sim K^{-\gamma}$ with $\gamma = 1+\ln M /\ln (M-1)$, (ii) the diameter grows logarithmically as $D \sim \ln N$ with the number of nodes $N$, (iii) the clustering coefficient of each node is inversely proportional to its degree, $C \propto 1/K$, and the average clustering coefficient is nonzero in the infinite $N$ limit, and (iv) the betweenness centrality distribution follows a power law $P_B \sim B^{-2}$. We discuss a classification scheme of scale-free networks into the universality class with the clustering property and the betweenness centrality distribution.Comment: 4 page

Ferromagnetic phase transition and Bose-Einstein condensation in spinor Bose gases

Phase transitions in spinor Bose gases with ferromagnetic (FM) couplings are studied via mean-field theory. We show that an infinitesimal value of the coupling can induce a FM phase transition at a finite temperature always above the critical temperature of Bose-Einstein condensation. This contrasts sharply with the case of Fermi gases, in which the Stoner coupling $I_s$ can not lead to a FM phase transition unless it is larger than a threshold value $I_0$. The FM coupling also increases the critical temperatures of both the ferromagnetic transition and the Bose-Einstein condensation.Comment: 4 pages, 4 figure