A Note on the Holographic Beta and C Functions

The holographic RG flow in AdS/CFT correspondence naturally defines a holographic scheme in which the central charge c and the beta function are related by a universal formula. We perform some checks of that formula and we compare it with quantum field theory expectations. We discuss alternative definitions of the c-function. In particular, we compare, for a particular supersymmetric flow, the holographic c-function with the central charge computed directly from the two-point function of the stress-energy tensor.Comment: Version accepted for publication in Phys. Lett. B, expanded introduction. 11 pages, 2 embedded eps figure

Minimal Higgs Branch for the Breaking of Half of the Supersymmetries in N=2 Supergravity

It is shown that the minimal Higgs sector of a generic N=2 supergravity theory with unbroken N=1 supersymmetry must contain a Higgs hypermultiplet and a vector multiplet. When the multiplets parametrize the quaternionic manifold SO(4,1)/SO(4), and the special Kahler manifold SU(1,1)/U(1), respectively, a vanishing vacuum energy with a sliding massive spin 3/2 multiplet is obtained. Potential applications to N=2 low energy effective actions of superstrings are briefly discussed.Comment: 7 pages, plain Late

Heterotic-Type II String Duality and the H-Monopole Problem

Since T-duality has been proved only perturbatively and most of the heterotic states map into solitonic, non-perturbative, type II states, the 6-dimensional string-string duality between the heterotic string and the type II string is not sufficient to prove the S-duality of the former, in terms of the known T-duality of the latter. We nevertheless show in detail that perturbative T-duality, together with the heterotic-type II duality, does imply the existence of heterotic H-monopoles, with the correct multiplicity and multiplet structure. This construction is valid at a generic point in the moduli space of heterotic toroidal compactifications.Comment: 12 pages, plain Late

Novel Local CFT and Exact Results on Perturbations of N=4 Super Yang Mills from AdS Dynamics

We find new, local, non-supersymmetric conformal field theories obtained by relevant deformations of the N=4 super Yang Mills theory in the large $N$ limit. We contruct interpolating supergravity solutions that naturally represent the flow from the N=4 super Yang Mills UV theory to these non-supersymmetric IR fixed points. We also study the linearization around the N=4 superconformal point of N=1 supersymmetric, marginal deformations. We show that they give rise to N=1 superconformal fixed points, as expected from field-theoretical arguments.Comment: Version accepted by JHE

Confinement and Condensates Without Fine Tuning in Supergravity Duals of Gauge Theories

We discuss a solution of the equations of motion of five-dimensional gauged type IIB supergravity that describes confining SU(N) gauge theories at large N and large 't Hooft parameter. We prove confinement by computing the Wilson loop, and we show that our solution is generic, independent of most of the details of the theory. In particular, the Einstein-frame metric near its singularity, and the condensates of scalar, composite operators are universal. Also universal is the discreteness of the glueball mass spectrum and the existence of a mass gap. The metric is also identical to a generically confining solution recently found in type 0B theory.Comment: 19 pages, Late

Partial N=2 --> N=1 Local Supersymmetry Breaking and Solvable Lie Algebras

Generic partial supersymmetry breaking of N=2 supergravity with zero vacuum energy and with surviving unbroken arbitrary gauge groups is exhibited. Specific examples are given.Comment: 5 pages, 1 LaTeX-style file, 1 TeX, 2 Postscript figures. Seminar given at the Work-Shop on "Gauge Theories, Applied Supersymmetry and Quantum Gravity", Imperial College, London, 5-10 July 199

ALE manifolds and Conformal Field Theory

We address the problem of constructing the family of (4,4) theories associated with the sigma-model on a parametrized family ${\cal M}_{\zeta}$ of Asymptotically Locally Euclidean (ALE) manifolds. We rely on the ADE classification of these manifolds and on their construction as HyperK\"ahler quotients, due to Kronheimer. So doing we are able to define the family of (4,4) theories corresponding to a ${\cal M}_{\zeta}$ family of ALE manifolds as the deformation of a solvable orbifold ${\bf C}^2 \, / \, \Gamma$ conformal field-theory, $\Gamma$ being a Kleinian group. We discuss the relation among the algebraic structure underlying the topological and metric properties of self-dual 4-manifolds and the algebraic properties of non-rational (4,4)-theories admitting an infinite spectrum of primary fields. In particular, we identify the Hirzebruch signature $\tau$ with the dimension of the local polynomial ring {\cal R}=\o {{\bf C}[x,y,z]}{\partial W} associated with the ADE singularity, with the number of non-trivial conjugacy classes in the corresponding Kleinian group and with the number of short representations of the (4,4)-theory minus four.Comment: 48 pages, Latex, SISSA/44/92/EP, IFUM/443/F

Butterfly abundance in a warming climate: patterns in space and time are not congruent

We present a model of butterfly abundance on transects in England. The model indicates a significant role for climate, but the direction of association is counter to expectation: butterfly population density is higher on sites with a cooler climate. However, the effect is highly heterogeneous, with one in five species displaying a net positive association. We use this model to project the population-level effects of climate warming for the year 2080, using a medium emissions scenario. The results suggest that most populations and species will decline markedly, but that the total number of butterflies will increase as communities become dominated by a few common species. In particular, Maniola jurtina is predicted to make up nearly half of all butterflies on UK Butterfly Monitoring Scheme (UKBMS) transects by 2080. These results contradict the accepted wisdom that most insect populations will grow as the climate becomes warmer. Indeed, our predictions contrast strongly with those derived from inter-annual variation in abundance, emphasizing that we lack a mechanistic understanding about the factors driving butterfly population dynamics over large spatial and temporal scales. Our study underscores the difficulty of predicting future population trends and reveals the naivety of simple space-for-time substitutions, which our projections share with species distribution modelling

D-Brane Interactions in a Gravitational Shock Wave Background

We study D-branes in the background of a gravitational shock wave. We consider the case of parallel D-branes located on opposite sides with respect to the shock wave. Their interaction is studied by evaluating the cylinder diagram using the boundary states technique. Boundary states are defined at each D-brane and their scalar product is evaluated after propagation through the shock wave. Taking the limit where the gravitational shock wave vanishes we show that the amplitude evaluated is consistent with the flat space-time result.Comment: To be published in Modern Physics Letters A, revised version with references added, 12 page